Question

Solve the equation.
3(x + 8) = 2(3x + 24)
X= ?

Answer 1

Answer: x= 1 /2 or x= −8

Explanation:

Step 1: Simplify both sides of the equation.

3x+24=6x2+48x

Step 2: Subtract 6x^2+48x from both sides.

3x+24−(6x2+48x)=6x2+48x−(6x2+48x)

Step 3: Factor left side of equation.

−3(2x−1)(x+8)=0

Step 4: Set factors equal to 0. 2x−1=0 or x+8=0 x= 1 /2 or x=−8

Answer 2

x = -8

Explanation:

Solve for x:

3 (x + 8) = 2 (3 x + 24)

Expand out terms of the left hand side:

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

Expand out terms of the right hand side:

3 x + 24 = 6 x + 48

Subtract 6 x from both sides:

(3 x - 6 x) + 24 = (6 x - 6 x) + 48

3 x - 6 x = -3 x:

-3 x + 24 = (6 x - 6 x) + 48

6 x - 6 x = 0:

24 - 3 x = 48

Subtract 24 from both sides:

(24 - 24) - 3 x = 48 - 24

24 - 24 = 0:

-3 x = 48 - 24

48 - 24 = 24:

-3 x = 24

Divide both sides of -3 x = 24 by -3:

(-3 x)/(-3) = 24/(-3)

(-3)/(-3) = 1:

x = 24/(-3)

The gcd of 24 and -3 is 3, so 24/(-3) = (3×8)/(3 (-1)) = 3/3×8/(-1) = 8/(-1):

x = 8/(-1)

Multiply numerator and denominator of 8/(-1) by -1:

Answer: x = -8