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DISTANCE,CIRCLES,AND QUADRATIC EQUATIONS
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Quadratic and Rational Inequalit
Applications of Systems of Linear Equations in Two Variables
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Test Description for RATIONAL EX
Exponential and Logarithmic Equations
Systems of Linear Equations: Cramer's Rule
Introduction to Systems of Linear Equations
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Rational Expressions
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Steepest Descent for Solving Linear Equations
The Quadratic Equation
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Solve Two-Step Equations

Goal: Solve two-step equations.

Your Notes

IDENTIFYING OPERATIONS

Identify the operations involved in the equation

Operations performed on x Operations to isolate x
1. Multiply by 3 .
2. Add 7 .
1. Subtract 7 .
2. Divide by 3 .

Example 1 Multiple Choice Practice

What is the value of x if

Solution

Write original equation.
Subtract 7 from each side.
Simplify.
Divide each side by 3 .
Simplify
The correct answer is A .
CHECK  
Write original equation
Substitute 4 for x.
Multiply 3 by 4.
Simplify. Solution checks.

Your Notes

Guided Practice Solve the two-step equation. Check your solution.

Example 2 Solve a two-step equation by combining like terms

Solve 4a + 3a = 63.

Solution

Write original equation.
Combine like terms.
Divide each side by 7 .
Simplify.

Guided Practice Solve the equation. Check your solution.

Your Notes

Example 3 Write an equation and solve

The value of y is 2 more than 4 times the value of x. Find x when y = 14.

Solution

Step 1 Write an equation  
y is 2 more than 4 times x.
Step 2 Solve the equation for x when y = 14.
Write original equation.
Substitute 14 for y.
Subtract 2 from each side.
Simplify.
Divide each side by 4 .
Simplify.
The value of x is 3 when y = 14 .
CHECK  
Write original function
Substitute 14 for y and 3 for x
Multiply 4 and 3 .
Simplify. Solution checks.

Guided Practice Solve the equation. Check your solution.

Homework

7. The value of y is 3 less than 6 times the value of x.
Find x when y = 15.

x = 3

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