Answer :
To solve the equation [tex]\(-\frac{1}{2} x + 4 = x + 1\)[/tex], you can follow these steps:
1. Start with the given equation:
[tex]\[
-\frac{1}{2} x + 4 = x + 1
\][/tex]
2. Move all terms to one side of the equation to set it to zero:
[tex]\[
-\frac{1}{2} x + 4 - x - 1 = 0
\][/tex]
3. Combine like terms:
- For the [tex]\(x\)[/tex] terms: The expression [tex]\(-\frac{1}{2} x - x\)[/tex] simplifies to [tex]\(-\frac{3}{2} x\)[/tex].
- For the constant terms: The expression [tex]\(4 - 1\)[/tex] simplifies to [tex]\(3\)[/tex].
So, the equation becomes:
[tex]\[
-\frac{3}{2} x + 3 = 0
\][/tex]
4. Isolate the [tex]\(x\)[/tex] term:
[tex]\[
-\frac{3}{2} x = -3
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = -3 \div \left(-\frac{3}{2}\right)
\][/tex]
Simplifying the division:
[tex]\[
x = -3 \times \left(-\frac{2}{3}\right) = 2
\][/tex]
6. Therefore, the solution to the equation [tex]\( -\frac{1}{2} x + 4 = x + 1 \)[/tex] is:
[tex]\[
x = 2
\][/tex]
This means that the point where the two lines [tex]\(y = -\frac{1}{2} x + 4\)[/tex] and [tex]\(y = x + 1\)[/tex] intersect is at [tex]\(x = 2\)[/tex].
1. Start with the given equation:
[tex]\[
-\frac{1}{2} x + 4 = x + 1
\][/tex]
2. Move all terms to one side of the equation to set it to zero:
[tex]\[
-\frac{1}{2} x + 4 - x - 1 = 0
\][/tex]
3. Combine like terms:
- For the [tex]\(x\)[/tex] terms: The expression [tex]\(-\frac{1}{2} x - x\)[/tex] simplifies to [tex]\(-\frac{3}{2} x\)[/tex].
- For the constant terms: The expression [tex]\(4 - 1\)[/tex] simplifies to [tex]\(3\)[/tex].
So, the equation becomes:
[tex]\[
-\frac{3}{2} x + 3 = 0
\][/tex]
4. Isolate the [tex]\(x\)[/tex] term:
[tex]\[
-\frac{3}{2} x = -3
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = -3 \div \left(-\frac{3}{2}\right)
\][/tex]
Simplifying the division:
[tex]\[
x = -3 \times \left(-\frac{2}{3}\right) = 2
\][/tex]
6. Therefore, the solution to the equation [tex]\( -\frac{1}{2} x + 4 = x + 1 \)[/tex] is:
[tex]\[
x = 2
\][/tex]
This means that the point where the two lines [tex]\(y = -\frac{1}{2} x + 4\)[/tex] and [tex]\(y = x + 1\)[/tex] intersect is at [tex]\(x = 2\)[/tex].
