Answer :
To solve the inequality [tex]\(-24 \leq x - 3 - 8x\)[/tex], we need to follow a step-by-step approach to simplify the expression and isolate the variable [tex]\(x\)[/tex].
1. Simplify the expression on the right side of the inequality:
[tex]\[ -24 \leq x - 3 - 8x \][/tex]
Combine the like terms involving [tex]\(x\)[/tex]:
[tex]\[ -24 \leq -7x - 3 \][/tex]
2. Isolate the term involving [tex]\(x\)[/tex] by adding 3 to both sides of the inequality:
[tex]\[ -24 + 3 \leq -7x - 3 + 3 \][/tex]
Simplify both sides:
[tex]\[ -21 \leq -7x \][/tex]
3. Solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(-7\)[/tex]. Remember that dividing by a negative number reverses the inequality sign:
[tex]\[ \frac{-21}{-7} \geq x \][/tex]
Simplify:
[tex]\[ 3 \geq x \][/tex]
Or, equivalently:
[tex]\[ x \leq 3 \][/tex]
So the solution to the inequality [tex]\(-24 \leq x - 3 - 8x\)[/tex] is [tex]\(x \leq 3\)[/tex]. Therefore, the correct answer is:
D. [tex]\(x \leq 3\)[/tex]
1. Simplify the expression on the right side of the inequality:
[tex]\[ -24 \leq x - 3 - 8x \][/tex]
Combine the like terms involving [tex]\(x\)[/tex]:
[tex]\[ -24 \leq -7x - 3 \][/tex]
2. Isolate the term involving [tex]\(x\)[/tex] by adding 3 to both sides of the inequality:
[tex]\[ -24 + 3 \leq -7x - 3 + 3 \][/tex]
Simplify both sides:
[tex]\[ -21 \leq -7x \][/tex]
3. Solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(-7\)[/tex]. Remember that dividing by a negative number reverses the inequality sign:
[tex]\[ \frac{-21}{-7} \geq x \][/tex]
Simplify:
[tex]\[ 3 \geq x \][/tex]
Or, equivalently:
[tex]\[ x \leq 3 \][/tex]
So the solution to the inequality [tex]\(-24 \leq x - 3 - 8x\)[/tex] is [tex]\(x \leq 3\)[/tex]. Therefore, the correct answer is:
D. [tex]\(x \leq 3\)[/tex]
