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Answer :
To solve the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] using graphs, Michael plotted two equations:
1. [tex]\(y = -\frac{1}{2}x + 4\)[/tex]
2. [tex]\(y = x + 1\)[/tex]
The solution to the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] is the point where these two lines intersect on the graph.
Here's how to find the solution:
1. Set the equations equal to each other:
[tex]\[
-\frac{1}{2}x + 4 = x + 1
\][/tex]
2. Get all the [tex]\(x\)[/tex]-terms on one side:
To do this, subtract [tex]\(x\)[/tex] from both sides:
[tex]\[
-\frac{1}{2}x - x = 1 - 4
\][/tex]
3. Combine the [tex]\(x\)[/tex]-terms:
Notice that [tex]\(-\frac{1}{2}x - x\)[/tex] simplifies to [tex]\(-\frac{3}{2}x\)[/tex] or [tex]\(-1.5x\)[/tex]:
[tex]\[
-1.5x = -3
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by [tex]\(-1.5\)[/tex] to isolate [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-3}{-1.5} = 2.0
\][/tex]
5. Find the corresponding [tex]\(y\)[/tex] value:
Substitute [tex]\(x = 2.0\)[/tex] back into one of the original equations, say [tex]\(y = x + 1\)[/tex]:
[tex]\[
y = 2.0 + 1 = 3.0
\][/tex]
Thus, the solution to the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] is the point [tex]\((2.0, 3.0)\)[/tex]. This means the two lines intersect at this point on the graph.
1. [tex]\(y = -\frac{1}{2}x + 4\)[/tex]
2. [tex]\(y = x + 1\)[/tex]
The solution to the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] is the point where these two lines intersect on the graph.
Here's how to find the solution:
1. Set the equations equal to each other:
[tex]\[
-\frac{1}{2}x + 4 = x + 1
\][/tex]
2. Get all the [tex]\(x\)[/tex]-terms on one side:
To do this, subtract [tex]\(x\)[/tex] from both sides:
[tex]\[
-\frac{1}{2}x - x = 1 - 4
\][/tex]
3. Combine the [tex]\(x\)[/tex]-terms:
Notice that [tex]\(-\frac{1}{2}x - x\)[/tex] simplifies to [tex]\(-\frac{3}{2}x\)[/tex] or [tex]\(-1.5x\)[/tex]:
[tex]\[
-1.5x = -3
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by [tex]\(-1.5\)[/tex] to isolate [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-3}{-1.5} = 2.0
\][/tex]
5. Find the corresponding [tex]\(y\)[/tex] value:
Substitute [tex]\(x = 2.0\)[/tex] back into one of the original equations, say [tex]\(y = x + 1\)[/tex]:
[tex]\[
y = 2.0 + 1 = 3.0
\][/tex]
Thus, the solution to the equation [tex]\(-\frac{1}{2}x + 4 = x + 1\)[/tex] is the point [tex]\((2.0, 3.0)\)[/tex]. This means the two lines intersect at this point on the graph.
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