### All ACT Math Resources

## Example Questions

### Example Question #11 : How To Find A Solution Set

Given the follow inequality, which of the following presents a range of possible answers for the inequality: –3 < 3x + 2 ≤ 3.5

**Possible Answers:**

(–3, 1/2)

( –2, 2)

(–1,1)

(–1, ½)

(½, 1)

**Correct answer:**

(–1, ½)

If you plug in the outer limits of the given ranges, (–1, ½) is the only combination that fits within the given equation. It is important to remember that "<" means “less than,” and "≤" means “less than or equal.” For example, if you answered (–2,2), plugging in 2 would make the the expression equal 8, which is greater than 3.5. And plugging in –2 for x would make the expression equal –4, which is less than –3, not greater. However, plugging in the correct answer (–1, ½) gives you –1 as your lower limit and 3.5 as your upper limit, which satisfies the equation. Both limits of the data set must satisfy the equation.

### Example Question #12 : How To Find A Solution Set

If , what is the product of the largest and smallest integers that satisfy the inequality?

**Possible Answers:**

7

0

–10

–5

5

**Correct answer:**

0

The inequality in the question possesses an absolute value; therefore, we most solve for the variable being less than positive 6 and greater than negative 6. Let's start with the positive solution.

Add 4 to both sides of the inequality.

Divide both sides of the inequality by 2.

Now, let's solve for the negative solution

Add 4 to both sides of the inequality.

Divide both sides of the inequality by 2.

Using these solutions we can write the following statement:

The smallest integer that satisfies this equation is 0, and the largest is 4. Their product is 0.

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