1. Equations & Inequalities

Solve each problem. See Example 2. Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities to the nearest ten miles if his total traveling time was 32 hr?

Solve each problem. See Example 2. In the Apple Hill Fun Run, Mary runs at 7 mph, Janet at 5 mph. If they start at the same time, how long will it be before they are 1.5 mi apart?

Solve the Equation. $3\left(2-5x\right)=4x+25$

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation. $\frac{x}{4}+\frac16=\frac{x}{3}$

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation. 

$-2\left(5-3x\right)+x=7x-10$

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation. 

$5x+17=8x+12-3\left(x+4\right)$

Solve the equation.

$\frac92+\frac14\left(x+2\right)=\frac34x$

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation. 

$5x+17=8x+12-3(x+4)$

Solve and check each linear equation. 4x + 9 = 33

In Exercises 1–26, solve and check each linear equation. 7x - 5 = 72