Question

which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?

Explanation:

Step1: Expand the inequality

First, expand $3(8 - 4x)<6(x - 5)$. Using the distributive - property $a(b + c)=ab+ac$, we get $24-12x<6x - 30$.

Step2: Move the $x$ - terms to one side

Add $12x$ to both sides: $24<6x + 12x-30$, which simplifies to $24<18x - 30$.

Step3: Move the constant terms to one side

Add 30 to both sides: $24 + 30<18x$, so $54<18x$.

Step4: Solve for $x$

Divide both sides by 18: $\frac{54}{18} 3$.

Step5: Interpret the number - line

On a number - line, the solution $x>3$ is represented by an open circle at 3 (because 3 is not included in the solution set) and an arrow pointing to the right.

Answer:

The number - line with an open circle at 3 and an arrow pointing to the right represents the solution set.