Solving the inequality for x, which statement shows a good first step and which is the correct solution?

Question

x−6<x/4
(2 points)
Responses

Divide both sides of the inequality by 4 to simplify: x/4−3/2<x

Divide both sides of the inequality by 4 to simplify: x4−32<x

Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x

Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x

Divide both sides of the inequality by x to simplify: 1−6/x<4 x<6

Divide both sides of the inequality by x to simplify: 1−6x<4 x<6

Multiply both sides by x to get the "x" terms on the same side of the inequality: x−6<4

Multiply both sides by x to get the "x" terms on the same side of the inequality: x−6<4

Answer 1

To solve the inequality \( x - 6 < \frac{x}{4} \), the first step should ideally involve eliminating the fraction for simplicity. The best first step from the options given is:

"Multiply both sides by 4 to clear the inequality of fractions: \( 4(x - 6) < x \)"

This will yield: \[ 4x - 24 < x \] Now, to isolate \( x \), we will subtract \( x \) from both sides: \[ 4x - x - 24 < 0 \implies 3x - 24 < 0 \] Next, add 24 to both sides: \[ 3x < 24 \] Then, divide both sides by 3: \[ x < 8 \]

So the correct solution to the inequality \( x - 6 < \frac{x}{4} \) is:

\( x < 8 \).