(9x - 7) - (5x + 10 )
2x - 15x
- 13x
Given that GI = 53, and
• GH = 3x - 11
• HI = 2x + 4
We can establish the following equality statement to solve for x:
GH + HI = GI
3x - 11 + 2x + 4 = 53
Combine like terms:
5x - 7 = 53
Add 7 to both sides:
5x - 7 + 7 = 53 + 7
5x = 60
Divide both sides by 5 to solve for x:
5x/5 = 60/5
x = 12
Substitute the value of x into the equality statement to verify if it is the correct value for x:
GH + HI = GI
3x - 11 + 2x + 4 = 53
3(12) - 11 + 2(12) + 4 = 53
36 - 11 + 24 + 4 = 53
53 = 53 (True statement. Thus, x = 12 is the correct value).
Therefore:
GH = 3x - 11
GH = 3(12) - 11
GH = 25
HI = 2x + 4
HI = 2(12) + 4
HI = 28
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The answer is A. A perpendicular equation will have the opposite and reciprocal slope as the original equation.
Once converted to the slope-intercept form of y = mx+b, we find the two equations for A are y = 2x-1 and y = (-1/2)x + 3/2. The opposite reciprocal of the first equation's slope (m in the equation form given) is -1/2, which as you can see if the slope of the other equation.
