Exam 3: Equations, Inequalities and Problem Solving

The quotient of a number and five is 30 is translated as $\frac { 5 } { n } = 30$ .

Randall is following a 2,890-calorie-per-day diet plan. This plan permits 610 calories less than twice the number of calories permitted by Britney's diet plan. How many calories are permitted by Britney's plan? __________ calories

Use the properties of equality to solve the equation. $a - \frac { 2 } { 5 } = \frac { 2 } { 3 }$ Enter your answer in fraction form.

Use the properties of equality to solve the equation. $\frac { 5 } { 22 } m = \frac { 1 } { 11 }$

Solve the inequality. 8 z $-$ 5 6 z $-$ 9

Solve the inequality. $2 z + 5 \geq 8 z - 25$

Solve the equation. $7 p - 2 - 9 p = - 16$

Solve the equation. 3 ( x + 5) + 4 (2 x $-$ 8) = 5 (2 x + 1)

For the following problem, solve the inequality. $x + 18 \geq - 14$

Solve the equation. $7 n - 5 = 7 n - 4$

For the following problem, solve the inequality. 26 x < 156 Please enter your answer as an interval.

For the following problem, solve the inequality. x + 3 $-$ 18 Please enter your answer as an interval.

The multiplication-division property of equality states that an equivalent equation is obtained whenever both sides of a given equation are mulitplied or divided by the same real number.

For the following problem, solve the inequality. 7 x < 14 Please enter your answer as an interval.

Solve this equation. 20( k + 5) = 104

The plans for an apartment complex provided for 400 apartments, with each apartment having one, two, or three bedrooms. There were to be 28 more three-bedroom than one-bedroom apartments, and the number of two-bedroom apartments was to be 12 less than 2 times the number of one-bedroom apartments. How many apartments of each type were in the plans? Please enter your answer as three numbers, listed from least to greatest, separated by commas.

Solve the equation. 18 = $-$ 2 $-$ 5 a

Solve the equation. $-$ 1( y + 3) = 2

Solve the equation. $2 p + 18 + 7 p = 63$