Answer :
To solve the equation [tex]\(-\frac{1}{2} x + 4 = x + 1\)[/tex], let's go through the solution step-by-step. The goal is to find the value of [tex]\(x\)[/tex] that satisfies the equation.
1. Start with the original equation:
[tex]\[
-\frac{1}{2} x + 4 = x + 1
\][/tex]
2. Eliminate the fraction by multiplying every term by 2:
[tex]\[
2 \left(-\frac{1}{2} x + 4\right) = 2(x + 1)
\][/tex]
This simplifies to:
[tex]\[
-x + 8 = 2x + 2
\][/tex]
3. Get all terms involving [tex]\(x\)[/tex] on one side of the equation and constant terms on the other side:
Add [tex]\(x\)[/tex] to both sides:
[tex]\[
-x + 8 + x = 2x + 2 + x
\][/tex]
Which simplifies to:
[tex]\[
8 = 3x + 2
\][/tex]
4. Isolate the [tex]\(x\)[/tex]-term:
Subtract 2 from both sides:
[tex]\[
8 - 2 = 3x
\][/tex]
Which gives:
[tex]\[
6 = 3x
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
Divide both sides by 3:
[tex]\[
x = \frac{6}{3}
\][/tex]
Therefore:
[tex]\[
x = 2
\][/tex]
The solution to the equation [tex]\(-\frac{1}{2} x + 4 = x + 1\)[/tex] is [tex]\(x = 2\)[/tex].
1. Start with the original equation:
[tex]\[
-\frac{1}{2} x + 4 = x + 1
\][/tex]
2. Eliminate the fraction by multiplying every term by 2:
[tex]\[
2 \left(-\frac{1}{2} x + 4\right) = 2(x + 1)
\][/tex]
This simplifies to:
[tex]\[
-x + 8 = 2x + 2
\][/tex]
3. Get all terms involving [tex]\(x\)[/tex] on one side of the equation and constant terms on the other side:
Add [tex]\(x\)[/tex] to both sides:
[tex]\[
-x + 8 + x = 2x + 2 + x
\][/tex]
Which simplifies to:
[tex]\[
8 = 3x + 2
\][/tex]
4. Isolate the [tex]\(x\)[/tex]-term:
Subtract 2 from both sides:
[tex]\[
8 - 2 = 3x
\][/tex]
Which gives:
[tex]\[
6 = 3x
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
Divide both sides by 3:
[tex]\[
x = \frac{6}{3}
\][/tex]
Therefore:
[tex]\[
x = 2
\][/tex]
The solution to the equation [tex]\(-\frac{1}{2} x + 4 = x + 1\)[/tex] is [tex]\(x = 2\)[/tex].
