Certainly! Let’s solve the equation [tex]\(15 - 4(3x + 1) = 1 + 4(2x + 20)\)[/tex] step by step.
1. Expand both sides:
First, we expand the parentheses on both sides of the equation.
Left-hand side:
[tex]\[
15 - 4(3x + 1) = 15 - 12x - 4
\][/tex]
Simplify by combining like terms:
[tex]\[
15 - 4 - 12x = 11 - 12x
\][/tex]
Right-hand side:
[tex]\[
1 + 4(2x + 20) = 1 + 8x + 80
\][/tex]
Simplify by combining like terms:
[tex]\[
1 + 80 + 8x = 81 + 8x
\][/tex]
2. Set the expanded left-hand side equal to the expanded right-hand side:
[tex]\[
11 - 12x = 81 + 8x
\][/tex]
3. Isolate the variable [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we need to get all the terms involving [tex]\(x\)[/tex] on one side of the equation and the constants on the other side.
First, add [tex]\(12x\)[/tex] to both sides to get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[
11 = 81 + 8x + 12x
\][/tex]
Simplify:
[tex]\[
11 = 81 + 20x
\][/tex]
Next, subtract 81 from both sides to move the constant term:
[tex]\[
11 - 81 = 20x
\][/tex]
Simplify:
[tex]\[
-70 = 20x
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by 20 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-70}{20} = -\frac{7}{2}
\][/tex]
Therefore, the solution to the equation [tex]\(15 - 4(3x + 1) = 1 + 4(2x + 20)\)[/tex] is:
[tex]\[ x = -\frac{7}{2} \][/tex]
