Certainly! Let's solve the equation [tex]\( 4(x + 21) = -3(x - 7) \)[/tex] step-by-step.
1. Distribute the constants on both sides:
On the left side:
[tex]\[
4(x + 21) = 4x + 4 \cdot 21 = 4x + 84
\][/tex]
On the right side:
[tex]\[
-3(x - 7) = -3x + (-3) \cdot (-7) = -3x + 21
\][/tex]
So, the equation becomes:
[tex]\[
4x + 84 = -3x + 21
\][/tex]
2. Combine like terms:
To isolate the variable [tex]\(x\)[/tex], we need to get all the [tex]\(x\)[/tex]-terms on one side of the equation and the constants on the other. Start by adding [tex]\(3x\)[/tex] to both sides to combine the [tex]\(x\)[/tex]-terms:
[tex]\[
4x + 84 + 3x = -3x + 21 + 3x
\][/tex]
[tex]\[
7x + 84 = 21
\][/tex]
3. Isolate the [tex]\(x\)[/tex]-term:
Subtract 84 from both sides to move the constant term to the right side:
[tex]\[
7x + 84 - 84 = 21 - 84
\][/tex]
[tex]\[
7x = -63
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by 7 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-63}{7}
\][/tex]
[tex]\[
x = -9
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\( -9 \)[/tex]. Therefore, the correct answer is:
C. [tex]\(x = -9\)[/tex]
