Exam 3: Equations, Inequalities and Problem Solving

Raoul received a $25 tip for waiting on a large party. This was $10 more than one-fourth of the tip the head-waiter received. How much did the headwaiter get for a tip?

The solution of the compound inequality $x > - 3 \text { and } x < 2$ is $( - 3,2 )$ .

At a university-sponsored concert, there were 3 times as many women as men. A total of 160 people attended the concert. How many men and how many women attended?

For the following problem, solve the inequality. $22 x - 5 < 149$ Please enter your answer as an interval.

Which of the given graphs is the solution of the following compound inequality? $x \leq 6 \text { or } x \geq 9$

Solve the problem by setting up and solving an appropriate inequality. Patrick has scores of 88, 86, and 74 on his first three algebra tests. What score must he get on the fourth test to have an average of 80 or higher for the four tests? Please use the variable x in your answer.

Find three consecutive even numbers whose sum is 36.

For the following problem state the solution set. $x \leq - 13$ Please enter your answer as an interval.

Solve the inequality. $10 ( s - 2 ) < 12 ( s + 5 )$

The solution set for $\{ x \mid x \leq - 4 \}$ is written in interval notation as $[ - \infty , - 4 ]$ .

For the following problem state the solution set. x > 7 Please enter your answer as an interval.

Use the properties of equality to solve the equation. $- \frac { 3 } { 16 } a = 1$

Solve the inequality. $\frac { x - 1 } { 2 } + \frac { x + 8 } { 15 } > \frac { 1 } { 30 }$

Solve the inequality. $19 x + 7 > 19 x + 3$

Use the properties of equality to solve the equation. 5 t = $-$ 30

Solve the inequality. $\frac { z - 1 } { 7 } + \frac { z + 1 } { 6 } > \frac { 1 } { 42 }$

Solve this equation. Simplify your answer. $\frac { k } { 15 } + \frac { k } { 35 } = 1$ Do not convert fractions to decimal form.

Use the properties of equality to solve the equation. $-$ 17 = u + 15

Find the largest of three consecutive whole numbers such that twice the sum of the two smallest numbers is 10 more than three times the largest number.

For the following problem, solve the inequality. 28 x Please enter your answer as an interval.