Solve the inequality:

[tex]\[ 4(-2x + 1) \geq -12 \][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution is [tex]\(\square\)[/tex]
(Type an inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.)

B. The solution is all real numbers.

C. There is no solution.



Answer :

To solve the inequality [tex]\( 4(-2x + 1) \geq -12 \)[/tex], let's follow a step-by-step approach:

1. Distribute the 4:
[tex]\[ 4 \cdot (-2x + 1) \geq -12 \][/tex]
This simplifies to:
[tex]\[ 4 \cdot (-2x) + 4 \cdot 1 \geq -12 \][/tex]
[tex]\[ -8x + 4 \geq -12 \][/tex]

2. Isolate the term involving [tex]\(x\)[/tex]:
To isolate the term involving [tex]\(x\)[/tex], subtract 4 from both sides of the inequality:
[tex]\[ -8x + 4 - 4 \geq -12 - 4 \][/tex]
Simplifying this gives:
[tex]\[ -8x \geq -16 \][/tex]

3. Solve for [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], divide both sides by -8. Remember, when you divide by a negative number, the inequality sign flips:
[tex]\[ \frac{-8x}{-8} \leq \frac{-16}{-8} \][/tex]
Simplifying this gives:
[tex]\[ x \leq 2 \][/tex]

So, the correct choice is:
A. The solution is [tex]\( x \leq 2 \)[/tex]

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