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QuestionSolve for xx in the equation: x−10+12x+5+3x−85=180x - 10 + \frac{1}{2} x + 5 + 3 x - 85 = 180.

Studdy Solution

STEP 1

Assumptions1. The equation is x−10+1x+5+3x−85=180x-10+\frac{1}{} x+5+3 x-85 =180 . We are to solve for xx
3. The equation is linear and therefore has a unique solution

STEP 2

First, we need to simplify the equation by combining like terms. The like terms in this equation are the terms with xx and the constant terms.
x+12x+x−10+5−85=180x + \frac{1}{2}x +x -10 +5 -85 =180

STEP 3

Combine the terms with xx.
(1+12+3)x=180+10−5+85\left(1 + \frac{1}{2} +3\right)x =180 +10 -5 +85

STEP 4

implify the left side of the equation.
(32+4)x=180+10−+85\left(\frac{3}{2} +4\right)x =180 +10 - +85

STEP 5

Continue simplifying the left side of the equation.
(82)x=180+10−5+85\left(\frac{8}{2}\right)x =180 +10 -5 +85

STEP 6

implify the right side of the equation.
4x=180+10−5+854x =180 +10 -5 +85

STEP 7

Continue simplifying the right side of the equation.
4x=2704x =270

STEP 8

Now that we have simplified the equation, we can solve for xx by dividing both sides of the equation by4.
x=2704x = \frac{270}{4}

STEP 9

implify the right side of the equation to find the value of xx.
x=67.5x =67.5The solution to the equation is x=67.5x =67.5.

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