Solve the inequality [tex]-24 \leq x - 3 - 8x[/tex].

A. [tex]x \geq 3[/tex]
B. [tex]x \geq -3[/tex]
C. [tex]x \geq -9[/tex]
D. [tex]x \leq 3[/tex]



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]