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Answer :
To solve the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex], we need to find the value of [tex]\(x\)[/tex] that makes both sides equal.
Here are the steps to solve the equation:
1. Move the terms involving [tex]\(x\)[/tex] to one side of the equation:
Start by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the [tex]\(x\)[/tex]-term from the left side. The equation becomes:
[tex]\[
4 = x + \frac{1}{2}x + 1
\][/tex]
2. Combine like terms on the right side:
Combine [tex]\(x\)[/tex] and [tex]\(\frac{1}{2}x\)[/tex] on the right side:
[tex]\[
x + \frac{1}{2}x = \frac{3}{2}x
\][/tex]
So now, the equation is:
[tex]\[
4 = \frac{3}{2}x + 1
\][/tex]
3. Isolate the [tex]\(x\)[/tex]-term:
Subtract 1 from both sides to isolate the [tex]\(\frac{3}{2}x\)[/tex] term on the right:
[tex]\[
4 - 1 = \frac{3}{2}x
\][/tex]
[tex]\[
3 = \frac{3}{2}x
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], divide both sides by [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
x = \frac{3}{3/2}
\][/tex]
5. Simplify the division:
Dividing 3 by [tex]\(\frac{3}{2}\)[/tex] is the same as multiplying 3 by the reciprocal of [tex]\(\frac{3}{2}\)[/tex], which is [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
x = 3 \times \frac{2}{3} = 2
\][/tex]
So, the solution to the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] is [tex]\(x = 2\)[/tex].
Here are the steps to solve the equation:
1. Move the terms involving [tex]\(x\)[/tex] to one side of the equation:
Start by adding [tex]\(\frac{1}{2}x\)[/tex] to both sides to eliminate the [tex]\(x\)[/tex]-term from the left side. The equation becomes:
[tex]\[
4 = x + \frac{1}{2}x + 1
\][/tex]
2. Combine like terms on the right side:
Combine [tex]\(x\)[/tex] and [tex]\(\frac{1}{2}x\)[/tex] on the right side:
[tex]\[
x + \frac{1}{2}x = \frac{3}{2}x
\][/tex]
So now, the equation is:
[tex]\[
4 = \frac{3}{2}x + 1
\][/tex]
3. Isolate the [tex]\(x\)[/tex]-term:
Subtract 1 from both sides to isolate the [tex]\(\frac{3}{2}x\)[/tex] term on the right:
[tex]\[
4 - 1 = \frac{3}{2}x
\][/tex]
[tex]\[
3 = \frac{3}{2}x
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], divide both sides by [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
x = \frac{3}{3/2}
\][/tex]
5. Simplify the division:
Dividing 3 by [tex]\(\frac{3}{2}\)[/tex] is the same as multiplying 3 by the reciprocal of [tex]\(\frac{3}{2}\)[/tex], which is [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
x = 3 \times \frac{2}{3} = 2
\][/tex]
So, the solution to the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] is [tex]\(x = 2\)[/tex].
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