To solve the equation [tex]\(\frac{1}{4}(16+12x)=28\)[/tex], we will use the distributive property first.
The equivalent equation is found by distributing the [tex]\(\frac{1}{4}\)[/tex] to get:
[tex]\[
\frac{1}{4} \cdot 16 + \frac{1}{4} \cdot 12x
\][/tex]
This simplifies to:
[tex]\[
4 + 3x
\][/tex]
The first step is:
[tex]\[
4 + 3x = 28
\][/tex]
The second step is to isolate [tex]\(x\)[/tex]. We do this by subtracting 4 from both sides:
[tex]\[
4 + 3x - 4 = 28 - 4
\][/tex]
This simplifies to:
[tex]\[
3x = 24
\][/tex]
Next, we divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{24}{3}
\][/tex]
This simplifies to:
[tex]\[
x = 8
\][/tex]
So, the detailed steps are:
1. [tex]\(\frac{1}{4}(16+12x)=28\)[/tex]
2. Distribute the [tex]\(\frac{1}{4}\)[/tex] to get: [tex]\(4+3x=28\)[/tex]
3. Subtract 4 from both sides: [tex]\(3x=24\)[/tex]
4. Divide by 3 to solve for [tex]\(x\)[/tex]: [tex]\(x=8\)[/tex]
The answer is:
[tex]\[
x = 8
\][/tex]
