Answer :
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]
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]