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What is the solution to [tex][tex]$-4(8 - 3x) \geq 6x - 8$[/tex][/tex]?

A. [tex][tex]$x \geq \frac{4}{3}$[/tex][/tex]
B. [tex][tex]$x \leq -\frac{4}{3}$[/tex][/tex]
C. [tex][tex]$x \geq 4$[/tex][/tex]
D. [tex][tex]$x \leq 4$[/tex][/tex]



Answer :

GinnyAnswer
To solve the inequality [tex]\(-4(8 - 3x) \geq 6x - 8\)[/tex], let's follow a step-by-step process:

1. Distribute the [tex]\(-4\)[/tex] on the left side of the inequality:

[tex]\[ -4(8 - 3x) \geq 6x - 8 \][/tex]

This gives us:

[tex]\[ -4 \cdot 8 + (-4) \cdot (-3x) \geq 6x - 8 \][/tex]

Simplifying further:

[tex]\[ -32 + 12x \geq 6x - 8 \][/tex]

2. Combine like terms:

To simplify, let's move all the terms involving [tex]\(x\)[/tex] to one side and constant terms to the other side. Subtract [tex]\(6x\)[/tex] from both sides:

[tex]\[ -32 + 12x - 6x \geq -8 \][/tex]

Simplifying, we get:

[tex]\[ -32 + 6x \geq -8 \][/tex]

3. Isolate the [tex]\(x\)[/tex] term:

Now, add 32 to both sides to isolate the [tex]\(x\)[/tex] term:

[tex]\[ -32 + 6x + 32 \geq -8 + 32 \][/tex]

Simplifying, we have:

[tex]\[ 6x \geq 24 \][/tex]

4. Solve for [tex]\(x\)[/tex]:

Finally, divide both sides by 6:

[tex]\[ x \geq \frac{24}{6} \][/tex]

Which simplifies to:

[tex]\[ x \geq 4 \][/tex]

So, the solution to the inequality [tex]\(-4(8 - 3x) \geq 6x - 8\)[/tex] is:

[tex]\[ x \geq 4 \][/tex]

The correct answer is:

[tex]\[ x \geq 4 \][/tex]

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