Answered

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What value of [tex]$x$[/tex] is in the solution set of the inequality [tex]$4x - 12 \leq 16 + 8x$[/tex]?

A. [tex][tex]$-10$[/tex][/tex]
B. [tex]$-9$[/tex]
C. [tex]$-8$[/tex]
D. [tex][tex]$-7$[/tex][/tex]

Sagot :

GinnyAnswer
To determine which value of [tex]\(x\)[/tex] satisfies the inequality [tex]\(4x - 12 \leq 16 + 8x\)[/tex], we will solve the inequality step by step.

1. Start with the original inequality:
[tex]\[ 4x - 12 \leq 16 + 8x \][/tex]

2. Subtract [tex]\(4x\)[/tex] from both sides to isolate the variable [tex]\(x\)[/tex] on one side:
[tex]\[ -12 \leq 16 + 4x \][/tex]

3. Subtract 16 from both sides to further isolate the term involving [tex]\(x\)[/tex]:
[tex]\[ -28 \leq 4x \][/tex]

4. Divide both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[ -7 \leq x \][/tex]

This can also be written as:
[tex]\[ x \geq -7 \][/tex]

Now we need to check which of the given values satisfies [tex]\(x \geq -7\)[/tex]:

- For [tex]\(x = -10\)[/tex]:
[tex]\[ -10 \not\geq -7 \quad \Rightarrow \text{Not a solution} \][/tex]

- For [tex]\(x = -9\)[/tex]:
[tex]\[ -9 \not\geq -7 \quad \Rightarrow \text{Not a solution} \][/tex]

- For [tex]\(x = -8\)[/tex]:
[tex]\[ -8 \not\geq -7 \quad \Rightarrow \text{Not a solution} \][/tex]

- For [tex]\(x = -7\)[/tex]:
[tex]\[ -7 \geq -7 \quad \Rightarrow \text{Solution} \][/tex]

Therefore, the value in the solution set of the inequality [tex]\(4x - 12 \leq 16 + 8x\)[/tex] is:
[tex]\[ -7 \][/tex]
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