Pre Algebra Solving Linear Equations in One Variable

University:
Virtual High School
Course:
STEM | Mathematics
Academic year:

2020
Views:

245

Pages:

4
Author:

Edgar Rowe

Pre Algebra Study Guide Solving Linear Equations in One Variable Solving Two-Step Equations with Rational Coefficients ● The goal of solving an equation is to isolate the variable, or get a variable alone on one side of the equation. ● A two-step equation contains two operations. To solve a two-step equation use the inverse operations and properties of equality to isolate the variable. Addition and subtraction are inverse operations. Multiplication and division are inverse operations. ● To solve an equation when the coefficient of the variable is a fraction: Solving Multi-Step Equations To solve an equation, isolate the variable. ● If the equation has parentheses, use the Distributive Property. ● Combine like terms on each side of the equation, as needed. ● Use the properties of equality and inverse operations to isolate the variable. ● Check your solution. Solving Equations with Variables on Both Sides To solve an equation, you need to isolate the variable. ● If the equation has parentheses, use the Distributive Property ● If there are like terms on the same side of the equation, combine like terms. ● Collect all the variables onto one side of the equation using inverse operations. ● Collect all the constants on the other side by using inverse operations Solutions of One Variable Equations When solving an equation with variables on both sides, you can find: ● One Solution- When you solve the equation, the solution will be a variable equal to a number (x=a, with a being a constant) ● Infinitely many solutions- When you solve the equation, the variable will cancel itself out, and your solution will be a true statement, where an answer equals itself (a=a, with a being a constant) and the solution will make the equation true. ● No solution- When solving an equation, the variable cancels out, but you get a false statement where two numbers are not equal (a=b, with a and b both representing two different constants). The equation has no true number solution. Solving Equations Containing Fractions by Clearing the Fraction Clearing the Fraction: If an equation contains fractions, you should clear the fraction using the steps below: 1. Find the Least Common Denominator (LCD) of the fractions. 2. Multiple every term on both sides of the equation by the LCD 3. Simplify the fractions 4. Solve the equation Solving Linear Equations by Solving Proportions ● Linear equations made up of the equivalent rational expressions are solved the same way we normally solve proportions. ● When there is more than one term in the numerator or/and denominator, put the expression with more than one term in parentheses so that you remember to use the distributive property when transforming the equation. Applications of Linear Equations 1. The sum of thirteen and twice a number is seven less than six times a number. What is the number? Let x= the number 2. The sum of four consecutive integers is -26. What are the integers? Let x= 1st integer Let x+1= 2nd integer Let x+2= 3rd integer Let x+3= 4th integer