Answer :

GinnyAnswer
Sure, let's solve the equation step by step.

Given:
[tex]\[ \frac{3(8x + 24)}{12} = 9 - 3(x - 4) \][/tex]

Step 1: Simplify the left side of the equation

First, distribute the 3 inside the parentheses:
[tex]\[ 3(8x + 24) = 3 \cdot 8x + 3 \cdot 24 = 24x + 72 \][/tex]

Then, divide by 12:
[tex]\[ \frac{24x + 72}{12} = \frac{24x}{12} + \frac{72}{12} = 2x + 6 \][/tex]

So, the left side of the equation simplifies to:
[tex]\[ 2x + 6 \][/tex]

Step 2: Simplify the right side of the equation

First, distribute the [tex]\(-3\)[/tex] inside the parentheses:
[tex]\[ -3(x - 4) = -3x + 12 \][/tex]

Then add the 9:
[tex]\[ 9 - 3x + 12 = -3x + 21 \][/tex]

So, the right side of the equation simplifies to:
[tex]\[ -3x + 21 \][/tex]

Step 3: Combine the simplified expressions

Now the equation is:
[tex]\[ 2x + 6 = -3x + 21 \][/tex]

Step 4: Combine like terms

Add [tex]\(3x\)[/tex] to both sides to get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[ 2x + 3x + 6 = 21 \][/tex]
[tex]\[ 5x + 6 = 21 \][/tex]

Subtract 6 from both sides to isolate the [tex]\(x\)[/tex]-term:
[tex]\[ 5x = 21 - 6 \][/tex]
[tex]\[ 5x = 15 \][/tex]

Step 5: Solve for [tex]\(x\)[/tex]

Finally, divide by 5:
[tex]\[ x = \frac{15}{5} \][/tex]
[tex]\[ x = 3 \][/tex]

So, the solution is:
[tex]\[ x = 3 \][/tex]

Other Questions