Solving the inequality for x, which statement shows a good first step and which is the correct solution?
x−6<x4
x
−
6
<
x
4
(2 points)
Responses
Divide both sides of the inequality by x to simplify: 1−6x<4
1
−
6
x
<
4
x<6
x
<
6
Divide both sides of the inequality by x to simplify: 1−6x<4
1
−
6
x
<
4
x<6
x
<
6
Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x
4
x
−
24
<
x
Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x
4
x
−
24
<
x
Divide both sides of the inequality by 4 to simplify: x4−32<x
x
4
−
3
2
<
x
Divide both sides of the inequality by 4 to simplify: x4−32<x
x
4
−
3
2
<
x
Multiply both sides by x to get the "x" terms on the same side of the inequality:
No
Apologies for the misunderstanding. Let me clarify the steps and provide the correct solutions:
Given inequality: x - 6 < x/4
To solve this inequality, we can follow these steps:
Step 1: Move all the terms involving x to one side of the inequality:
x - x/4 < 6
Step 2: Combine the x terms on the left side:
(4x - x)/4 < 6
Step 3: Simplify the left side:
3x/4 < 6
Step 4: Multiply both sides of the inequality by 4 to eliminate the fraction:
4 * (3x/4) < 4 * 6
3x < 24
Step 5: Divide both sides of the inequality by 3 to isolate x:
(3x)/3 < 24/3
x < 8
So, the correct solution to the inequality is x < 8.
Answering it using one of the following
Responses
Divide both sides of the inequality by x to simplify: 1−6x<4
1
−
6
x
<
4
x<6
x
<
6
Divide both sides of the inequality by x to simplify: 1−6x<4
1
−
6
x
<
4
x<6
x
<
6
Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x
4
x
−
24
<
x
Multiply both sides by 4 to clear the inequality of fractions: 4x−24<x
4
x
−
24
<
x
Divide both sides of the inequality by 4 to simplify: x4−32<x
x
4
−
3
2
<
x
Divide both sides of the inequality by 4 to simplify: x4−32<x
x
4
−
3
2
<
x
Multiply both sides by x to get the "x" terms on the same side of the inequality: x−6<4
x
−
6
<
4
To solve the inequality x - 6 < x/4, you would perform the following steps:
1. Subtract x from both sides of the inequality to get rid of the x term on the right side:
x - x - 6 < x/4 - x
-6 < -3x/4
2. Multiply both sides of the inequality by -4/3 to get rid of the fraction:
-6 * (-4/3) > (-3x/4) * (-4/3)
8 > x
The correct solution is x > 8, which can be represented as x > 8.
The correct first step is to divide both sides of the inequality by x to simplify it: 1−6x<4.
The correct solution is x<6.