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
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
Divide both sides of the inequality by x to simplify: 1−6/x<4
x<6
The correct response is: Divide both sides of the inequality by x to simplify: 1-6/x<4
To solve the inequality x-6<x/4, let's go step-by-step.
Step 1: Divide both sides of the inequality by 4 to simplify: x/4 - 6/4 < x/4
Step 2: Simplify the left side by subtracting 6/4: x/4 - 3/2 < x/4
Step 3: Multiply both sides by 4 to clear the inequality of fractions: 4(x/4 - 3/2) < 4(x/4)
Step 4: Simplify both sides: x - 6 < x
Step 5: Subtract x from both sides to get the "x" terms on the same side of the inequality: x - x - 6 < x - x
Step 6: Simplify: -6 < 0
Step 7: The inequality -6 < 0 is always true, so the solution is all real numbers.
Therefore, x can be any real number.