University:
Glendale Community College
Course:
MAT142 | College Mathematics
Academic year:

2019
Views:

426

Pages:

2
Author:

izbra0p

Section 2.1: Linear equations Chapter 2: Functions, Linear equations, and inequalities Solving Linear Equations 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. For example: Solve, be sure to check your answer. (These problems only require step 3 and step 5, or step 4 and step 5. Neither of these problems require steps 1 or 2.) Solve: 𝑥 – 7 = 13 Requires steps 3 & 5 Solve: 2𝑥 = 12 Requires steps 4 & 5 Step 3: 𝑥 − 7 = 13 +7 + 7 Answer: 𝑥 = 20 Step 4: Step 5: Check, replace 𝑥 with 20 in original problem and confirm the sides of the equation are equal after simplifying. 20 – 7 = 13 13 = 13 ✓ 2𝑥 2 12 = 2 Answer: 𝑥 = 6 Step 5: Check 2(6) = 12 12 = 12 ✓ For example: Solve, be sure to check your answer. (This problem will require steps 3, 4 and 5. It will not require step 1 nor 2.) Solve: 3x – 8 = 22 Step 3: 3𝑥 − 8 = 22 +8 + 8 3x = 30 For example: Solve, be sure to check your answer. (This problem will require all 5 steps.) Solve: 2𝑥 + 3(8𝑥 − 14) = 4 + 3𝑥 Step 1: First clear parenthesis: 2𝑥 + 24𝑥 – 42 = 4 + 3𝑥 Next combine 2𝑥 + 24𝑥 Step 4: 26𝑥 – 42 = 4 + 3𝑥 3𝑥 3 Step 2: Get the x-terms on the left side. = 30 3 Answer: 𝑥 = 10 Step 5: Check 3(10) – 8 = 22 30 – 8 = 22 22 = 22 ✓ 26𝑥 – 42 = 4 + 3𝑥 −3𝑥 − 3𝑥 23𝑥 – 42 = 4 Step 3: Get the numbers without the variables on the right side. 23𝑥 – 42 = 4 +42 + 42 23𝑥 = 46 Step 4: 23𝑥 46 = 23 23 Answer: 𝑥 = 2 Step 5: Check 2(2) + 3(8(2) − 14) = 4 + 3(2) 2(2) + 3(2) = 4 + 3(2) 4 + 6 = 4 + 6 10 = 10 ✓