Answer :
To solve the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex], we need to find the value of [tex]\(x\)[/tex] where the two equations [tex]\(y = -\frac{1}{2}x + 4\)[/tex] and [tex]\(y = x + 1\)[/tex] intersect.
Here's a step-by-step approach to solve it:
1. Start with the given equation:
[tex]\[
-\frac{1}{2}x + 4 = x + 1
\][/tex]
2. To eliminate the fraction, it's helpful to multiply the entire equation by 2 to make calculations easier:
[tex]\[
-x + 8 = 2x + 2
\][/tex]
3. To isolate [tex]\(x\)[/tex] on one side, add [tex]\(x\)[/tex] to both sides of the equation:
[tex]\[
8 = 3x + 2
\][/tex]
4. Next, subtract 2 from both sides to move the constant term to the other side:
[tex]\[
6 = 3x
\][/tex]
5. Finally, divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = 2
\][/tex]
Therefore, the solution to the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] is [tex]\(x = 2\)[/tex]. This means the two lines intersect at [tex]\(x = 2\)[/tex].
Here's a step-by-step approach to solve it:
1. Start with the given equation:
[tex]\[
-\frac{1}{2}x + 4 = x + 1
\][/tex]
2. To eliminate the fraction, it's helpful to multiply the entire equation by 2 to make calculations easier:
[tex]\[
-x + 8 = 2x + 2
\][/tex]
3. To isolate [tex]\(x\)[/tex] on one side, add [tex]\(x\)[/tex] to both sides of the equation:
[tex]\[
8 = 3x + 2
\][/tex]
4. Next, subtract 2 from both sides to move the constant term to the other side:
[tex]\[
6 = 3x
\][/tex]
5. Finally, divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = 2
\][/tex]
Therefore, the solution to the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] is [tex]\(x = 2\)[/tex]. This means the two lines intersect at [tex]\(x = 2\)[/tex].
