ACT Math : Solution Sets
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Example Question #11 : Solution Sets
Given the follow inequality, which of the following presents a range of possible answers for the inequality: –3 < 3x + 2 ≤ 3.5
( –2, 2)
(–3, 1/2)
(½, 1)
(–1, ½)
(–1,1)
(–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 : Solution Sets
If 
0
–10
–5
5
7
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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