Question

1.5(x−2)−3(2−x)

2.3(2x−7)+ 1/3 (7x+2)

Please help me! the online H.W is marking me wrong and I only have 2 attempts left!

Answer 1

1. x = 2

2. x = 61/25

Explanation:

Solve for x:

5 (x - 2) - 3 (2 - x) = 0

-3 (2 - x) = 3 x - 6:

3 x - 6 + 5 (x - 2) = 0

5 (x - 2) = 5 x - 10:

5 x - 10 + 3 x - 6 = 0

Grouping like terms, 5 x + 3 x - 10 - 6 = (3 x + 5 x) + (-6 - 10):

(3 x + 5 x) + (-6 - 10) = 0

3 x + 5 x = 8 x:

8 x + (-6 - 10) = 0

-6 - 10 = -16:

8 x + -16 = 0

Add 16 to both sides:

8 x + (16 - 16) = 16

16 - 16 = 0:

8 x = 16

Divide both sides of 8 x = 16 by 8:

(8 x)/8 = 16/8

8/8 = 1:

x = 16/8

The gcd of 16 and 8 is 8, so 16/8 = (8×2)/(8×1) = 8/8×2 = 2:

Answer: x = 2

_____________________________

Solve for x:

Solve for x:

3 (2 x - 7) + (7 x + 2)/3 = 0

Put each term in 3 (2 x - 7) + (7 x + 2)/3 over the common denominator 3: 3 (2 x - 7) + (7 x + 2)/3 = (9 (2 x - 7))/3 + (7 x + 2)/3:

(9 (2 x - 7))/3 + (7 x + 2)/3 = 0

(9 (2 x - 7))/3 + (7 x + 2)/3 = (9 (2 x - 7) + (7 x + 2))/3:

(9 (2 x - 7) + 2 + 7 x)/3 = 0

9 (2 x - 7) = 18 x - 63:

(18 x - 63 + 7 x + 2)/3 = 0

Grouping like terms, 18 x + 7 x - 63 + 2 = (18 x + 7 x) + (2 - 63):

((18 x + 7 x) + (2 - 63))/3 = 0

18 x + 7 x = 25 x:

(25 x + (2 - 63))/3 = 0

2 - 63 = -61:

(25 x + -61)/3 = 0

Multiply both sides of (25 x - 61)/3 = 0 by 3:

(3 (25 x - 61))/3 = 3×0

(3 (25 x - 61))/3 = 3/3×(25 x - 61) = 25 x - 61:

25 x - 61 = 3×0

0×3 = 0:

25 x - 61 = 0

Add 61 to both sides:

25 x + (61 - 61) = 61

61 - 61 = 0:

25 x = 61

Divide both sides of 25 x = 61 by 25:

(25 x)/25 = 61/25

25/25 = 1:

Answer: x = 61/25