Answer is 11/90
Step by step
7 1/2x - 1/4 = 2/3
Add 1/4 to both sides to isolate variable x
7 1/2x - 1/4 + 1/4 = 2/3 + 1/4
Simplify
7 1/2x = 2/3 + 1/4
Let’s look at the fractions we need to add.
The denominator needs to be the same to add or subtract fractions.
2/3 + 1/4.
12 is the number divisible by 3 and 4 so it’s the common denominator (bottom number)
To change each fraction to the same denominator, multiply the bottom number by a number to result in 12, then multiply the top by the same number.
2/3 x 4/4 = 8/12
1/4 x 3/3 = 3/12
Now add
8/12 + 3/12 = 11/12
7 1/2x = 11/12
Divide both sides by 7 1/2 to solve for x
First, Let’s change 7 1/2 into an improper fraction by multiplying 7 x 2 + 1 = 15/2
15/2 / 15/2 x = 11/12 / 15/2
15/2 / 15/2 x = 1x
To divide 11/12 / 15/2, flip the divisor and multiply
11/12 x 2/15 = 22/ 180
Simplify your fraction by dividing both parts by 2
11/90 is your final answer