Solve 1/4x−3/4>5 1/4

Question

options:

x > 21 and 3 over 4

x > 1 and 1 over 2

x > 18

x > 24

Answer 1

To solve the inequality 1/4x - 3/4 > 5 1/4, we need to isolate the variable x.

First, let's simplify the right side of the inequality:

5 1/4 = 4 + 1/4 = 16/4 + 1/4 = 17/4

Now, let's simplify the left side of the inequality:

1/4x - 3/4

To combine the fractions, we need a common denominator, which is 4:

1/4x - 3/4 = (1x - 3)/4

Now, the inequality becomes:

(1x - 3)/4 > 17/4

To eliminate the fraction, we can multiply both sides of the inequality by 4:

(4)(1x - 3)/4 > (4)(17/4)
x - 3 > 17

Next, we can simplify the equation:
x > 17 + 3
x > 20

So, the solution to the inequality is x > 20.

Among the given options, the correct choice is:
x > 21 and 3 over 4.