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Difficulty: MediumSolving Linear Equations

If the equation 25(x−4)+13(2x+k)=7\frac{2}{5}(x - 4) + \frac{1}{3}(2x + k) = 7 is true when x=9x = 9, what is the value of kk?

  1. A
    −17-17
  2. B
    11
  3. −3-3Answer
  4. D
    33
  5. E
    88

Answer

−3-3
Substituting x=9x = 9 into the equation gives 25(9−4)+13(2(9)+k)=7\frac{2}{5}(9 - 4) + \frac{1}{3}(2(9) + k) = 7. Simplifying the terms yields 2+18+k3=72 + \frac{18 + k}{3} = 7. Subtracting 2 from both sides results in 18+k3=5\frac{18 + k}{3} = 5. Multiplying by 3 gives 18+k=1518 + k = 15. Subtracting 18 from both sides gives k=−3k = -3.

Step-by-Step Solution

1
Substitute x=9x = 9 into the given equation.
25(9−4)+13(2(9)+k)=7\frac{2}{5}(9 - 4) + \frac{1}{3}(2(9) + k) = 7
We are given that the equation is true when x=9x = 9.
2
Simplify the operations inside the parentheses.
2+18+k3=72 + \frac{18 + k}{3} = 7
Simplifying 25(5)\frac{2}{5}(5) gives 2, and 2(9)2(9) gives 18.
3
Subtract 2 from both sides of the equation.
18+k3=5\frac{18 + k}{3} = 5
Isolating the fraction term simplifies the equation.
4
Multiply both sides by 3.
18+k=1518 + k = 15
Clearing the denominator allows us to isolate the variable kk.
5
Subtract 18 from both sides of the equation.
k=−3k = -3
This isolates kk to find its value.

Key Concept

Solving linear equations in one variable by substitution and simplification
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Topics

Solving Linear Equations

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