Answer :
To find the solution to the equation [tex]\( -\frac{1}{2} x + 4 = x + 1 \)[/tex], you can follow these steps:
1. Move all terms involving [tex]\( x \)[/tex] to one side of the equation:
[tex]\[ -\frac{1}{2} x + 4 = x + 1 \][/tex]
Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[ -\frac{1}{2} x - x + 4 = 1 \][/tex]
2. Combine like terms:
[tex]\[ -\frac{1}{2} x - x = -\frac{1}{2} x - \frac{2}{2} x = -\frac{3}{2} x \][/tex]
So the equation now is:
[tex]\[ -\frac{3}{2} x + 4 = 1 \][/tex]
3. Move the constant term to the other side of the equation by subtracting 4 from both sides:
[tex]\[ -\frac{3}{2} x + 4 - 4 = 1 - 4 \][/tex]
[tex]\[ -\frac{3}{2} x = -3 \][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by [tex]\( -\frac{3}{2} \)[/tex]:
[tex]\[ x = \frac{-3}{-\frac{3}{2}} \][/tex]
5. Simplify the fraction:
[tex]\[ x = -3 \div -\frac{3}{2} = -3 \times -\frac{2}{3} = 2 \][/tex]
So the solution to the equation [tex]\( -\frac{1}{2} x + 4 = x + 1 \)[/tex] is [tex]\( x = 2 \)[/tex].
This means that the two lines [tex]\( y = -\frac{1}{2} x + 4 \)[/tex] and [tex]\( y = x + 1 \)[/tex] intersect at the point where [tex]\( x = 2 \)[/tex].
1. Move all terms involving [tex]\( x \)[/tex] to one side of the equation:
[tex]\[ -\frac{1}{2} x + 4 = x + 1 \][/tex]
Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[ -\frac{1}{2} x - x + 4 = 1 \][/tex]
2. Combine like terms:
[tex]\[ -\frac{1}{2} x - x = -\frac{1}{2} x - \frac{2}{2} x = -\frac{3}{2} x \][/tex]
So the equation now is:
[tex]\[ -\frac{3}{2} x + 4 = 1 \][/tex]
3. Move the constant term to the other side of the equation by subtracting 4 from both sides:
[tex]\[ -\frac{3}{2} x + 4 - 4 = 1 - 4 \][/tex]
[tex]\[ -\frac{3}{2} x = -3 \][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by [tex]\( -\frac{3}{2} \)[/tex]:
[tex]\[ x = \frac{-3}{-\frac{3}{2}} \][/tex]
5. Simplify the fraction:
[tex]\[ x = -3 \div -\frac{3}{2} = -3 \times -\frac{2}{3} = 2 \][/tex]
So the solution to the equation [tex]\( -\frac{1}{2} x + 4 = x + 1 \)[/tex] is [tex]\( x = 2 \)[/tex].
This means that the two lines [tex]\( y = -\frac{1}{2} x + 4 \)[/tex] and [tex]\( y = x + 1 \)[/tex] intersect at the point where [tex]\( x = 2 \)[/tex].
