Equations / Inequalities

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ACT Math › Equations / Inequalities

Questions 1 - 10

Simplify

Explanation

Simplifying an inequality like this is very simple. You merely need to treat it like an equation—just don't forget to keep the inequality sign.

First, subtract from both sides:

Then, divide by :

3x + 9i2 – 5x = 17

What is x?

–13

–4

–1

Explanation

i = $\sqrt{-1}$

i2 = -1

3x + 9i2 – 5x = 17

3x + 9(–1) – 5x = 17

–2x – 9 = 17

–2x = 26

x = –13

Solve the following inequality:

Explanation

To solve an equality that has addition, simply treat it as an equation. Remember, the only time you have to do something to the inquality is when you are multiplying or dividing by a negative number.

Subrtract 4 from each side. Thus,

Two cars start 25 mile apart and drive away from each other in opposite directions at speeds of 50 and 70 miles per hour. In approximately how many minutes will they be 400 miles apart?

None of the other answers

187.5

200

3.33

3.125

Explanation

The cars have a distance from each other of 25 + 120t miles, where t is the number of hours, 25 is their initial distance and 120 is 50 + 70, or their combined speeds. Solve this equation for 400:

25 + 120t = 400; 120t = 375; t = 3.125

However, the question asked for minutes, so we must multiply this by 60:

3.125 * 60 = 187.5 minutes.

Simplify

Explanation

Simplifying an inequality like this is very simple. You merely need to treat it like an equation—just don't forget to keep the inequality sign.

First, subtract from both sides:

Then, divide by :

A certain number squared, plus four times itself is equal to zero.

Which of the following could be that number?

Explanation

The sentence should first be translated into an equation.

We will call the "certain number" .

This gives us $x^{2}+4x=0$ .

So solve this we can factor out an to get .

This makes the zeros of the equation evident. We know that when the entire expression will equal zero, making the equation true. We also know that when , the quantity will be , which also satisfies the equation.

Therefore, the two possible solutions are and .

Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.

If Pets Plus sells 50 bird houses, what is the profit?

$\$500$

$\$250$

$\$750$

$\$300$

$\$625$

Explanation

Let $x$ = the number of birdhouses sold each month.

$Revenue=40x$

$Costs=15x+750$

$Profit = Revenue-Costs$

$=40x-15x-750$

$=25x-750$

Substituting in 50 for $x$ gives an answer of 500, so the profit on 50 birdhouses is $500.

A car averages miles per gallon. If gas costs $\$ 3.04$ per gallon, which of the following is closest to how much the gas would cost for this car to travel $1\textup{,}642$ typical miles?

$\$156$

$\$50$

$\$51$

$\$155$

$\$17$

Explanation

To solve this problem you should divide the total number of miles $\left ( 1\textup{,}642\right )$ by the miles per gallon $\left ( 32\right )$ , and then multiply by the cost of gas per gallon $\left ( \$3.04\right)$ . This gives you $\$155.99$ , which is closest to $\$156$ .