Question

3(3-3x)=2(x+3)-30 solve and check solution

Answer 1

x = 3

Explanation:

Solve for x:

3 (3 - 3 x) = 2 (x + 3) - 30

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

3 (3 - 3 x) = 2 x + 6 - 30

Grouping like terms, 2 x - 30 + 6 = 2 x + (6 - 30):

3 (3 - 3 x) = 2 x + (6 - 30)

6 - 30 = -24:

3 (3 - 3 x) = 2 x + -24

Expand out terms of the left hand side:

9 - 9 x = 2 x - 24

Subtract 2 x from both sides:

9 + (-9 x - 2 x) = (2 x - 2 x) - 24

-9 x - 2 x = -11 x:

-11 x + 9 = (2 x - 2 x) - 24

2 x - 2 x = 0:

9 - 11 x = -24

Subtract 9 from both sides:

(9 - 9) - 11 x = -9 - 24

9 - 9 = 0:

-11 x = -9 - 24

-9 - 24 = -33:

-11 x = -33

Divide both sides of -11 x = -33 by -11:

(-11 x)/(-11) = (-33)/(-11)

(-11)/(-11) = 1:

x = (-33)/(-11)

The gcd of -33 and -11 is -11, so (-33)/(-11) = (-11×3)/(-11×1) = (-11)/(-11)×3 = 3:

Answer: x = 3

Answer 2

x = 3

Explanation:

Solve:

3(3 - 3x) = 2(x + 3) – 30 Remove parentheses

9 – 9x = 2x + 6 – 30 Combine like terms

9 – 9x = 2x – 24 Add 24 to each side

33 – 9x = 2x Add 9x to each side

33 = 11x Divide each side by 11

x = 3

Check:

3(3 - 3x) = 2(x + 3) – 30

3(3 – 3×3) = 2(3+ 3) – 30

3(3 – 9) = 2×6 – 30

3(-6) = 12 – 30

-18 = -18