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QuestionSolve the equation: 0.95x−0.99=12.93−3.85x0.95 x - 0.99 = 12.93 - 3.85 x. What is xx? A. x=□x=\square, B. all real numbers, C. no solution.

Studdy Solution

STEP 1

Assumptions1. The given equation is 0.95x−0.99=12.93−3.85x0.95x -0.99 =12.93 -3.85x . We are solving for xx
3. The equation is linear, so there should be one solution for xx

STEP 2

First, we need to isolate xx terms on one side of the equation and constants on the other side. Let's start by adding .85x.85x to both sides of the equation.
0.95x+.85x=12.93−0.99+.85x0.95x +.85x =12.93 -0.99 +.85x

STEP 3

implify the left side of the equation by adding the xx terms together.
.8x=12.93−0.99+3.85x.8x =12.93 -0.99 +3.85x

STEP 4

Now, simplify the right side of the equation by subtracting 0.990.99 from 12.9312.93.
4.8x=11.94+3.85x4.8x =11.94 +3.85x

STEP 5

To isolate xx terms on one side of the equation, subtract 3.85x3.85x from both sides of the equation.
4.8x−3.85x=11.944.8x -3.85x =11.94

STEP 6

implify the left side of the equation by subtracting the xx terms.
0.95x=11.940.95x =11.94

STEP 7

Now, to solve for xx, divide both sides of the equation by 0.950.95.
x=11.940.95x = \frac{11.94}{0.95}

STEP 8

Calculate the value of xx.
x=11.940.95=12.57x = \frac{11.94}{0.95} =12.57So, the solution to the equation is x=12.57x =12.57.

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