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Difficulty: MediumLinear Equations in One Variable

If 3(2.5x−4)−1.5(x−2)=0.8(5x+10)3(2.5x - 4) - 1.5(x - 2) = 0.8(5x + 10), what is the value of xx?

Answer: 8.5

Answer

8.5
By distributing and simplifying terms, the linear equation simplifies to 2x=172x = 17, which yields x=8.5x = 8.5.

Step-by-Step Solution

1
Distribute the constants on both sides of the equation.
7.5x−12−1.5x+3=4x+87.5x - 12 - 1.5x + 3 = 4x + 8
To simplify the expressions.
2
Combine like terms on the left side.
6x−9=4x+86x - 9 = 4x + 8
To simplify the left side of the equation.
3
Subtract 4x4x from both sides of the equation.
2x−9=82x - 9 = 8
To group variable terms on one side.
4
Add 9 to both sides of the equation.
2x=172x = 17
To isolate the term with the variable.
5
Divide both sides by 2.
x=8.5x = 8.5
To find the final value of the variable.

Key Concept

Linear Equations in One Variable

Alternative Method

Multiply the entire equation by 10 to clear all decimal values: 30(2.5x−4)−15(x−2)=8(5x+10)30(2.5x - 4) - 15(x - 2) = 8(5x + 10). Expanding this yields 75x−120−15x+30=40x+8075x - 120 - 15x + 30 = 40x + 80, which simplifies to 60x−90=40x+8060x - 90 = 40x + 80. Subtracting 40x40x and adding 90 to both sides gives 20x=17020x = 170, resulting in x=8.5x = 8.5.
Estimated Time:1m 30s
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Topics

Linear Equations in One Variable

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