What value of x is in the solution set of 3(x - 4) \geqslant 5x + 2 A. -10 B. -5 C. 5 D. 10​

Question

What value of x is in the solution set of


`3(x - 4) \geqslant 5x + 2`
A. -10
B. -5
C. 5
D. 10​

Answer 1

Option A: x = -10 is a solution.

Explanation:

Here we have the inequality:

3*(x - 4) ≥ 5*x + 2

We can solve this for x as follows:

first, expand the left side:

3x - 12 ≥ 5x + 2

now, move all the terms with x to one side, and the other terms to the other side:

-12 - 2 ≥ 5x - 3x

-14 ≥ 2x

now let's divide both sides by 2

-14/2 ≥ 2x/2

-7 ≥ x

So the solutions are values smaller than -7

In the options, the only value smaller than -7 is the first one:

A: -10

Then the correct option is A.