Warm-up

Jim makes $5.75 an hour. Each week, 26% of his total pay is deducted for taxes. Write an expression for the amount Jim has after taxes.

5.75h - .26(5.75h)4.255h

Creating Linear Equations and Inequalities in One Variable

Adapted from Walch

Standard

MCC9-12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and exponential functions.

Essential Question

How do I create equations and inequalities in one variable and use them to solve problems arising from linear and exponential functions?

Words to Know Equation Inequality Solution Solution set Variable

Equation

A mathematical sentence that uses an equal sign (=) to show that two quantities are equal.

Inequality

A mathematical sentence that shows the relationship between quantities that are not equivalent.

Solution

A value that makes an equation true.

The solution is x = 2

Solution set

The value or values that make a sentence or statement true.

The solution set is any number less than 2

Creating Equations or Inequalities from Context

1. Drawing a Sketch (if necessary)2. Defining a Variable (What is the

question asking)3. Setting up an equation or

inequality4. Solve the equation or inequality5. Make sure you answer the

question

ExampleJames earns $15 per hour as a teller at a bank. In one week he pays 17% of his earnings in state and federal taxes. His take-home pay for the week is $460.65. How many hours did James work?

ExampleIt cost Justin $100 to have cable TV installed in his house. Each month he pays an access fee plus tax of 7% of his monthly bill. After 6 months, Justin had paid a total of $350.38 for his access fee, taxes, and his initial installation. What is Justin’s monthly access fee not including taxes?

ExampleJuan has no more than $50 to spend at the mall. He wants to buy a pair of jeans and some juice. If the sales tax on the jeans is 4% and the juice with tax costs $2, what is the maximum price of jeans Juan can afford?