To solve the equation [tex]\(\frac{3}{2}+\frac{1}{2} x=2x\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Eliminate the fractions to simplify the equation:
- Note that the denominators are 2 in both fractions. To eliminate the fractions, multiply each term of the equation by 2:
[tex]\[
2 \left(\frac{3}{2}\right) + 2 \left(\frac{1}{2}x\right) = 2(2x)
\][/tex]
2. Simplify each term:
- Distribute the 2 across each term:
[tex]\[
3 + x = 4x
\][/tex]
Now a simpler linear equation is obtained:
[tex]\[
3 + x = 4x
\][/tex]
3. Isolate the variable [tex]\(x\)[/tex]:
- To isolate [tex]\(x\)[/tex], subtract [tex]\(x\)[/tex] from both sides of the equation:
[tex]\[
3 + x - x = 4x - x
\][/tex]
This simplifies to:
[tex]\[
3 = 3x
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Divide both sides of the equation by 3:
[tex]\[
x = \frac{3}{3} = 1
\][/tex]
Therefore, the solution is:
[tex]\[
x = 1
\][/tex]
