Section 2.1. Linear equations Chapter 2. Functions, Linear equations, and inequalities

Section 2.1: Linear equations Chapter 2: Functions, Linear equations, and inequalities #1 – 20: Solve, be sure to check your answer. (These problems only require step 3 and step 5, or step 4 and step 5. None of these problems require steps 1 and 2.) Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 1) 𝑥 + 5 = 10 Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 3) 𝑥 − 13 = 16 Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 1 5 2 2 5) 𝑥 + = Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 7) 𝑦 − 3 = 1 2 Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 9) 3𝑥 = 21 Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 11) −6𝑧 = 30 Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 13) 2 3 𝑥 = 18 15) 17) −4 5 4 7 𝑧 = 16 𝑥 = 10 19) −3 4 𝑧 = 13 #21 -44: Solve, be sure to check your answer. (These problems will require most of steps 2, 3, 4 and 5. They will not require step 1.) Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 21) 6𝑥 + 10 = 22 Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 23) 8𝑥 – 19 = 13 Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 25) 2 3 𝑥 + 24 = 30 Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 27) −2 3 𝑦 − 14 = −28 29) 15 = 3𝑥 + 18 31) −44 = 11𝑥 + 10 1 33) 22 = 𝑥 − 20 2 2 35) 17 = 3 𝑧 − 14 37) 8𝑥 + 30 = 5𝑥 39) 5𝑧 − 32 = −3𝑧 41) 4𝑥 = 5𝑥 − 12 43) 15𝑥 = 9𝑥 + 41 Section 2.1: Linear equations Chapter 2: Functions, Linear equations, and inequalities #45 – 64: Solve, be sure to check your answer. (These problems will require all 5 steps.) Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 45) 3𝑥 + 55 − 9𝑥 = 24 + 4𝑥 − 9 Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 47) 3𝑥 + 55 + 7 = 24𝑥 + 4𝑥 + 12 Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 49) 3(5𝑦 − 4) = 48 Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 51) −3(2𝑥 − 5) = −9 Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 53) 21 = −7(2𝑥 − 3) Steps to solve a linear equation: 1) Simplify each side of the equation as much as possible. • Use the Distributive Property to remove any parentheses. • Combine like terms when needed. 2) Collect all the variable terms on one side of the equation. • Add or subtract as needed 3) Collect all the constant terms on one side of the equation. • Add or subtract as needed 4) Make the coefficient of the variable term equal to 1. • Divide if the coefficient of the variable is an integer. • Multiply by the reciprocal if the coefficient of the variable is a fraction. 5) Check the solution. • Substitute the solution into the original equation to make sure the result is a true statement. 55) 5𝑥 + 3(6𝑥 − 7) = 25 57) 2𝑥 + 10 = 4(𝑥 − 1) + 8 59) 7𝑥 − 3(2𝑥 − 4) = 11𝑥 + 2 61) 8𝑥 − 3(𝑥 + 2) = 2(2𝑥 + 1) − 3 63) 16 = 8(2𝑥 + 1) − 5(2𝑥 + 2)