# MA.912.A.3.1 Solving Linear Equations

## Polynomials

Section 2-4 Pages 97-102

## What You Need To Know...

Solve linear equations in one variable including simplifying algebraic expressions.

1. The benchmark will be assessed using MC (Multiple Choice) and FR (Fill in Response) items.
2. Items may include applications of commutative, associative, distributive, and identity properties.
3. Items may have variables on both sides of the equal sign.

## Example One

Mario needs to cut three book shelves from a board that is 1.8 meters long.  The second shelf is 15 centimeters longer than twice the length of the first shelf.  The remaining shelf is 5 centimeters longer than the first shelf.  The equation below represents this situation, where x is the length of the first shelf in meters.

x + (2x + 0.15) + (x + 0.05) = 1.8

Which of the following is the length, in meters, of the first shelf?

A. 0.40

B. 0.45

C. 0.53

D. 0.96

## Example Two

Bill is planning to drive from his house to a baseball stadium and arrive in time for the beginning of the championship game.  His arrival time depends on the traffic.  If traffic is light, he will travel at an average speed of 50 miles per hour and arrive 1 hour early.  If traffic is heavy, he will travel at an average speed of 30 miles per hour and arrive on time.  The equation below can be used to model the situation, where t represents Bill's driving time in hours.

50(t    1) = 30t

What is the distance, in miles, from BIll's house to the baseball stadium?  The Distributive Property 