Question

Which values from this set {−30, −20, −10, 0, 10, 20} satisfy this inequality?

−1/5x+3≤7


A.−20, −10, 0, 10, and 20 only

B.0, 10, and 20 only

C.−30, −20, and −10 only

D.−30 and −20 only

Answer 1

Answer:  Choice A

-20, -10, 0, 10, and 20 only

In other words, everything but -30.

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Explanation:

Let's solve for x

$-\frac{1}{5}x + 3 \le 7\\\\-\frac{1}{5}x \le 7-3\\\\-\frac{1}{5}x \le 4\\\\x \ge 4*(-5)\\\\x \ge -20$

Note how the inequality sign flips when we multiply both sides by the negative number.

Since x can be -20 or larger, this means that the values -20,-10,0,10,20 are all solutions. Only -30 is a non-solution. It might help to draw out a number line to see which values work and don't work.

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An alternative method is to plug each value from the set {-30,-20,-10,0,10,20} into the original inequality and simplifying. If you get a true statement at the end, then the value is a solution.

I'll show an example with x = -30 and x = -20 to show a non-solution and a solution. I'll let you check the others.

So let's start with x = -30

$-\frac{1}{5}x + 3 \le 7\\\\-\frac{1}{5}(-30) + 3 \le 7\\\\6 + 3 \le 7\\\\9 \le 7$

The last statement is false because 9 is not 7 or smaller than 7. So that's why x = -30 is not a solution.

Now let's try x = -20

$-\frac{1}{5}x + 3 \le 7\\\\-\frac{1}{5}(-20) + 3 \le 7\\\\4 + 3 \le 7\\\\7 \le 7$

This is a true statement since any number is equal to itself.

You should find that x = -10, x = 0, x = 10, and x = 20 lead to true statements.