Question

Solve for x.

2(x−3 1/2)=10 3/4

Enter your answer as a mixed number in simplest form in the box.

Answer 1

x = 71/8

Explanation:

Solve for x:

2 (x - (3 + 1/2)) = 10 + 3/4

Put 3 + 1/2 over the common denominator 2. 3 + 1/2 = (2×3)/2 + 1/2:

2 (x - (7/2)) = 10 + 3/4

2×3 = 6:

2 (x - (1/2 6 + 1/2)) = 10 + 3/4

6/2 + 1/2 = (6 + 1)/2:

2 (x - (7/2)) = 10 + 3/4

6 + 1 = 7:

2 (x - 1/2 7) = 10 + 3/4

Put each term in x - 7/2 over the common denominator 2: x - 7/2 = (2 x)/2 - 7/2:

2 ((2 x)/2 - 7/2) = 10 + 3/4

(2 x)/2 - 7/2 = (2 x - 7)/2:

2 (1/2 (2 x - 7)) = 10 + 3/4

(2 (2 x - 7))/2 = 2/2×(2 x - 7) = 2 x - 7:

(2 x - 7) = 10 + 3/4

Put 10 + 3/4 over the common denominator 4. 10 + 3/4 = (4×10)/4 + 3/4:

2 x - 7 = ((4×10)/4 + 3/4)

4×10 = 40:

2 x - 7 = 40/4 + 3/4

40/4 + 3/4 = (40 + 3)/4:

2 x - 7 = ((40 + 3)/4)

40 + 3 = 43:

2 x - 7 = 43/4

Add 7 to both sides:

2 x + (7 - 7) = 43/4 + 7

7 - 7 = 0:

2 x = 43/4 + 7

Put 43/4 + 7 over the common denominator 4. 43/4 + 7 = 43/4 + (4×7)/4:

2 x = (43/4 + (4×7)/4)

4×7 = 28:

2 x = 43/4 + 28/4

43/4 + 28/4 = (43 + 28)/4:

2 x = ((43 + 28)/4)

43 + 28 = 71:

2 x = 71/4

Divide both sides by 2:

x = (71/2)/4

4×2 = 8:

Answer: x = 71/8