Question

1. consider $-2x - 9 \leq 5$. graph the solution set on the number line.

1. solve $\frac{3}{2}x < 9 - 6x$.

1. solve $10(x + 6.25) < 111$.

1. eileen needs at least $100 to buy a video game system. she earns $10 for each lawn she mows and has $15 in savings. write an inequality to determine how many lawns eileen must mow to buy the video game system.

$\underline{\quad\quad\quad\quad\quad\quad\quad} \leq \underline{\quad\quad\quad\quad\quad\quad\quad}x + \underline{\quad\quad\quad\quad\quad\quad\quad}$

1. trey has a 50 gallon water tank. he fills the tank with a garden hose at a rate of 4.4 gallons per minute. there are 6 gallons of water in the tank. what is the maximum amount of time trey can add water without causing the tank to overflow?

$\underline{\quad\quad\quad\quad\quad\quad\quad}$ minutes

Explanation:

Question 15

Step1: Add 9 to both sides

$-2x - 9 + 9 \leq 5 + 9$
$-2x \leq 14$

Step2: Divide by -2 (reverse inequality)

$\frac{-2x}{-2} \geq \frac{14}{-2}$
$x \geq -7$

To graph: Draw a closed circle at -7, shade to the right.

Step1: Add $6x$ to both sides

$\frac{3}{2}x + 6x < 9 - 6x + 6x$
$\frac{3}{2}x + \frac{12}{2}x < 9$
$\frac{15}{2}x < 9$

Step2: Multiply by $\frac{2}{15}$

$x < 9 \times \frac{2}{15}$
$x < \frac{18}{15}$
$x < \frac{6}{5}$ (or $1.2$)

Step1: Distribute 10

$10x + 10(6.25) < 111$
$10x + 62.5 < 111$

Step2: Subtract 62.5

$10x + 62.5 - 62.5 < 111 - 62.5$
$10x < 48.5$

Step3: Divide by 10

$x < \frac{48.5}{10}$
$x < 4.85$

Answer:

$x \geq -7$ (graph: closed circle at -7, right shade)

Question 16