Question

what is the solution to the inequality ( 4(3x + 1) - 8 geq 10 )?
a. ( x geq 2 )
b. ( x geq 4 )
c. ( x leq 4 )
d. ( x leq -4 )

Explanation:

Step1: Simplify the inequality

Start with the inequality \(4(3x + 1)-8\leq32\). First, distribute the 4: \(12x + 4-8\leq32\). Then combine like terms: \(12x-4\leq32\).

Step2: Isolate the variable term

Add 4 to both sides of the inequality: \(12x-4 + 4\leq32 + 4\), which simplifies to \(12x\leq36\).

Step3: Solve for x

Divide both sides by 12: \(\frac{12x}{12}\leq\frac{36}{12}\), so \(x\leq3\).

Answer:

Assuming the options are (for example, if option A is \(x\leq3\), then) A. \(x\leq3\) (Note: Since the original options' text was unclear, but following the solution, the correct inequality solution is \(x\leq3\), so match with the option that has \(x\leq3\))