Question

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

**\( x < 8 \)**.