To solve the equation [tex]\(\frac{3}{2} x + 1 = x + 4\)[/tex], we'll go through the following steps:
1. Isolate the variable term on one side:
Start by isolating the term involving [tex]\(x\)[/tex] on one side of the equation. To do this, we can subtract [tex]\(x\)[/tex] from both sides of the equation:
[tex]\[
\frac{3}{2} x + 1 - x = x + 4 - x
\][/tex]
Simplifying this step, we get:
[tex]\[
\frac{3}{2} x - x + 1 = 4
\][/tex]
2. Combine like terms:
Next, combine the [tex]\(x\)[/tex] terms on the left side:
[tex]\[
\frac{3}{2} x - \frac{2}{2} x + 1 = 4
\][/tex]
Simplifying the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{1}{2} x + 1 = 4
\][/tex]
3. Isolate [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], subtract 1 from both sides of the equation:
[tex]\[
\frac{1}{2} x + 1 - 1 = 4 - 1
\][/tex]
Simplifying this, we get:
[tex]\[
\frac{1}{2} x = 3
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], multiply both sides of the equation by 2:
[tex]\[
2 \cdot \frac{1}{2} x = 3 \cdot 2
\][/tex]
Simplifying this, we get:
[tex]\[
x = 6
\][/tex]
Therefore, the solution to the equation [tex]\(\frac{3}{2} x + 1 = x + 4\)[/tex] is [tex]\(x = 6\)[/tex].
