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Question Find the value of xx that satisfies the equation 0.75(x+20)=2+0.5(x−2)0.75(x+20)=2+0.5(x-2).

Studdy Solution

STEP 1

Assumptions1. The equation is 0.75(x+20)=+0.5(x−)0.75(x+20)=+0.5(x-). We are solving for the variable xx

STEP 2

First, we need to distribute the 0.750.75 on the left side of the equation and the 0.50.5 on the right side of the equation.
0.75x+0.75⋅20=2+0.5x−0.5⋅20.75x +0.75 \cdot20 =2 +0.5x -0.5 \cdot2

STEP 3

Now, calculate the products.
0.75x+15=2+0.5x−10.75x +15 =2 +0.5x -1

STEP 4

Next, simplify both sides of the equation.
0.75x+15=0.x+10.75x +15 =0.x +1

STEP 5

To isolate xx, we need to get all terms with xx on one side of the equation and the constants on the other side. Subtract 0.5x0.5x from both sides of the equation.
0.75x−0.5x+15=10.75x -0.5x +15 =1

STEP 6

Now, simplify the left side of the equation.
0.25x+15=10.25x +15 =1

STEP 7

Next, subtract 1515 from both sides of the equation to isolate the term with xx.
0.25x=1−150.25x =1 -15

STEP 8

Now, simplify the right side of the equation.
0.25x=−140.25x = -14

STEP 9

Finally, to solve for xx, divide both sides of the equation by .25.25.
x=−14/.25x = -14 /.25

STEP 10

Calculate the value of xx.
x=−56x = -56The value of xx that makes the equation true is −56-56.

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