Sure! Let's solve the equation [tex]\(\frac{1}{4}(4x - 24) + x = 14\)[/tex] step by step.
1. Distribute the [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
\frac{1}{4}(4x - 24) + x = 14
\][/tex]
Distributing [tex]\(\frac{1}{4}\)[/tex] to the terms inside the parentheses:
[tex]\[
\frac{1}{4} \cdot 4x - \frac{1}{4} \cdot 24 + x = 14
\][/tex]
Simplifying each term:
[tex]\[
x - 6 + x = 14
\][/tex]
2. Combine the like terms:
[tex]\[
x - 6 + x = 14
\][/tex]
Combining the [tex]\(x\)[/tex] terms:
[tex]\[
2x - 6 = 14
\][/tex]
3. Add 6 to both sides:
[tex]\[
2x - 6 + 6 = 14 + 6
\][/tex]
Simplifying:
[tex]\[
2x = 20
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by 2:
[tex]\[
x = \frac{20}{2}
\][/tex]
Simplifying:
[tex]\[
x = 10
\][/tex]
Therefore, the solution to the equation [tex]\(\frac{1}{4}(4x - 24) + x = 14\)[/tex] is [tex]\(x = 10\)[/tex].
