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Question Solve the linear equation 0.2(x+3)−4(2x−3)=0.90.2(x+3)-4(2x-3)=0.9 for the unknown variable xx.

Studdy Solution

STEP 1

Assumptions
1. We have the equation 0.2(x+3)−4(2x−3)=0.90.2(x+3)-4(2x-3)=0.9.
2. We need to solve for xx.

STEP 2

Distribute the 0.20.2 into the terms inside the first parenthesis and −4-4 into the terms inside the second parenthesis.
0.2(x)+0.2(3)−4(2x)+4(3)=0.90.2(x) + 0.2(3) - 4(2x) + 4(3) = 0.9

STEP 3

Perform the multiplication for each term.
0.2x+0.6−8x+12=0.90.2x + 0.6 - 8x + 12 = 0.9

STEP 4

Combine like terms on the left side of the equation.
−7.8x+12.6=0.9-7.8x + 12.6 = 0.9

STEP 5

Subtract 12.612.6 from both sides of the equation to isolate terms with xx on one side.
−7.8x+12.6−12.6=0.9−12.6-7.8x + 12.6 - 12.6 = 0.9 - 12.6

STEP 6

Perform the subtraction on both sides.
−7.8x=−11.7-7.8x = -11.7

STEP 7

Divide both sides by −7.8-7.8 to solve for xx.
−7.8x−7.8=−11.7−7.8\frac{-7.8x}{-7.8} = \frac{-11.7}{-7.8}

STEP 8

Calculate the value of xx.
x=−11.7−7.8x = \frac{-11.7}{-7.8}

STEP 9

Perform the division to find the value of xx.
x=1.5x = 1.5
The solution to the equation is x=1.5x = 1.5.

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