What is the value of $x$ if $-/frac23 (x-5) = / frac32 (x+1) $?

x = (-29) / 5

Step-by-step explanation:

Solve for x:

(2 (x - 5)) / 3 = (3 (x + 1)) / 2

Multiply both sides by 6:

(6*2 (x - 5)) / 3 = (6*3 (x + 1)) / 2

6/3 = (3*2) / 3 = 2:

2*2 (x - 5) = (6*3 (x + 1)) / 2

6/2 = (2*3) / 2 = 3:

2*2 (x - 5) = 3*3 (x + 1)

2*2 = 4:

4 (x - 5) = 3*3 (x + 1)

3*3 = 9:

4 (x - 5) = 9 (x + 1)

Expand out terms of the left hand side:

4 x - 20 = 9 (x + 1)

Expand out terms of the right hand side:

4 x - 20 = 9 x + 9

Subtract 9 x from both sides:

(4 x - 9 x) - 20 = (9 x - 9 x) + 9

4 x - 9 x = - 5 x:

-5 x - 20 = (9 x - 9 x) + 9

9 x - 9 x = 0:

-5 x - 20 = 9

Add 20 to both sides:

(20 - 20) - 5 x = 20 + 9

20 - 20 = 0:

-5 x = 9 + 20

9 + 20 = 29:

-5 x = 29

Divide both sides of - 5 x = 29 by - 5:

(-5 x) / (-5) = 29 / (-5)

(-5) / (-5) = 1:

x = 29 / (-5)

Multiply numerator and denominator of 29 / (-5) by - 1:

Answer: x = (-29) / 5