Answer :
To solve the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex], you can follow these steps:
1. Combine Like Terms: Start by getting all the [tex]\(x\)[/tex]-terms on one side of the equation. You can do this by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
-\frac{1}{2}x + \frac{1}{2}x + 4 = x + \frac{1}{2}x + 1
\][/tex]
This simplifies to:
[tex]\[
4 = \frac{3}{2}x + 1
\][/tex]
2. Isolate the Variable: Next, you need to isolate the [tex]\(x\)[/tex]-term. Subtract 1 from both sides to undo the addition:
[tex]\[
4 - 1 = \frac{3}{2}x
\][/tex]
Which simplifies to:
[tex]\[
3 = \frac{3}{2}x
\][/tex]
3. Solve for [tex]\(x\)[/tex]: Finally, solve for [tex]\(x\)[/tex] by multiplying both sides by the reciprocal of [tex]\(\frac{3}{2}\)[/tex], which is [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
x = 3 \times \frac{2}{3}
\][/tex]
Simplifying this gives:
[tex]\[
x = 2
\][/tex]
Therefore, the solution to the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] is [tex]\(x = 2\)[/tex].
1. Combine Like Terms: Start by getting all the [tex]\(x\)[/tex]-terms on one side of the equation. You can do this by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides:
[tex]\[
-\frac{1}{2}x + \frac{1}{2}x + 4 = x + \frac{1}{2}x + 1
\][/tex]
This simplifies to:
[tex]\[
4 = \frac{3}{2}x + 1
\][/tex]
2. Isolate the Variable: Next, you need to isolate the [tex]\(x\)[/tex]-term. Subtract 1 from both sides to undo the addition:
[tex]\[
4 - 1 = \frac{3}{2}x
\][/tex]
Which simplifies to:
[tex]\[
3 = \frac{3}{2}x
\][/tex]
3. Solve for [tex]\(x\)[/tex]: Finally, solve for [tex]\(x\)[/tex] by multiplying both sides by the reciprocal of [tex]\(\frac{3}{2}\)[/tex], which is [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
x = 3 \times \frac{2}{3}
\][/tex]
Simplifying this gives:
[tex]\[
x = 2
\][/tex]
Therefore, the solution to the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] is [tex]\(x = 2\)[/tex].
