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Difficulty: MediumLinear Equations in One Variable

If 5(2a−3)−3(4a−1)=−(a−8)5(2a - 3) - 3(4a - 1) = -(a - 8), what is the value of aa?

  1. A
    -10
  2. B
    -4
  3. -20Answer
  4. D
    -16

Answer

-20
Distributing the constants on both sides of the equation 5(2a−3)−3(4a−1)=−(a−8)5(2a - 3) - 3(4a - 1) = -(a - 8) yields 10a−15−12a+3=−a+810a - 15 - 12a + 3 = -a + 8. Combining like terms on the left side gives −2a−12=−a+8-2a - 12 = -a + 8. Adding 2a2a to both sides results in −12=a+8-12 = a + 8. Subtracting 88 from both sides gives the correct value of aa, which is −20-20.

Step-by-Step Solution

1
Distribute the coefficients to the terms inside the parentheses on both sides of the equation.
10a−15−12a+3=−a+810a - 15 - 12a + 3 = -a + 8
To eliminate parentheses and allow terms to be combined, apply the distributive property: 5(2a−3)=10a−155(2a - 3) = 10a - 15, −3(4a−1)=−12a+3-3(4a - 1) = -12a + 3, and −(a−8)=−a+8-(a - 8) = -a + 8.
2
Combine like terms on the left side of the equation.
−2a−12=−a+8-2a - 12 = -a + 8
Simplify the left side by combining the variable terms (10a−12a=−2a10a - 12a = -2a) and the constant terms (−15+3=−12-15 + 3 = -12).
3
Isolate the variable aa on one side of the equation.
a=−20a = -20
Add 2a2a to both sides of the equation to get −12=a+8-12 = a + 8, then subtract 88 from both sides to find that a=−20a = -20.

Key Concept

Solving linear equations in one variable using the distributive property, combining like terms, and isolating the variable.
Estimated Time:1m 30s
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Topics

Linear Equations in One Variable

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