Question

this question is worth 2 credits.
what value of x makes the equation shown below true?
24x + 33 = 3(5x + 21) - 9
show your work.

Explanation:

Step1: Expand the right side

First, we expand the right - hand side of the equation \(3(5x + 21)-9\) using the distributive property \(a(b + c)=ab+ac\).
\(3(5x+21)-9=3\times5x+3\times21 - 9=15x + 63-9\)
Then simplify the constants on the right - hand side: \(15x+(63 - 9)=15x+54\)
So the equation becomes \(24x + 33=15x+54\)

Step2: Subtract 15x from both sides

Subtract \(15x\) from both sides of the equation \(24x + 33=15x+54\) to get:
\(24x-15x + 33=15x-15x+54\)
Simplify the left - hand side and the right - hand side: \(9x+33 = 54\)

Step3: Subtract 33 from both sides

Subtract 33 from both sides of the equation \(9x + 33=54\):
\(9x+33 - 33=54 - 33\)
Simplify the left - hand side and the right - hand side: \(9x=21\)

Step4: Divide both sides by 9

Divide both sides of the equation \(9x = 21\) by 9:
\(x=\frac{21}{9}=\frac{7}{3}\)

Answer:

\(x = \frac{7}{3}\)