Question

What is the solution to –4(8 – 3x) ≥ 6x – 8?

x ≥ –x is greater than or equal to negative StartFraction 4 Over 3 EndFraction.
x ≤ –x is less than or equal to negative StartFraction 4 Over 3 EndFraction.
x ≥ 4
x ≤ 4

Answer 1

Answer:

$x\geq 4$

Step-by-step explanation:

Let's start by using distributive property to get rid of the parenthesis on the left hand side of the inequality:

$-4(8-3x)\geq 6x-8\\-32+12x\geq 6x-8$

Now let's group all the terms that contain the variable x on the left, and all pure numerical terms on the right of the inequality symbol. To accomplish such, we subtract 6x from both sides, and then add 32 to both sides:

$-32+12x\geq 6x-8\\-32+12x-6x\geq -8\\-32+6x\geq -8\\6x\geq -8+32\\6x\geq 24$

Now divide both sides of the inequality by positive 4 to isolate the "x" on one side:

$6x\geq 24\\x\geq \frac{24}{6} \\x\geq 4$

which agrees with the third option you listed.

Answer 2

Answer:

x ≥ 4

Step-by-step explanation:

The given inequality is

$-4(8-3x)\geq6x-8$

Distribute -4 over the parenthesis

$-32+12x\geq6x-8$

Subtract 6x to both sides

$-32+6x\geq-8$

Add 32 to both sides

$6x\geq24$

Divide both sides by 6

$x\geq4$

Thus, the solution is x ≥ 4