Examkin

Question

Difficulty: MediumSolving One-Variable Linear Equations

Solve the following linear equation for kk:

3−2(4k−5)=−5(k+1) 3 - 2(4k - 5) = -5(k + 1)

What is the exact value of kk?

  1. A
    00
  2. B
    −23-\frac{2}{3}
  3. 66Answer
  4. D
    83\frac{8}{3}

Answer

The correct value is 66.
The equation is correctly solved by first using the distributive property on both sides to get 3−8k+10=−5k−53 - 8k + 10 = -5k - 5. Combining the constants on the left side yields 13−8k=−5k−513 - 8k = -5k - 5. Adding 8k8k to both sides gives 13=3k−513 = 3k - 5. Finally, adding 55 to both sides results in 18=3k18 = 3k, and dividing by 33 gives the solution k=6k = 6.

Step-by-Step Solution

1
Distribute the coefficients into the parentheses on both sides of the equation.
3−8k+10=−5k−53 - 8k + 10 = -5k - 5
To eliminate the parentheses and expose all terms for simplification.
2
Combine the constant terms on the left side of the equation.
13−8k=−5k−513 - 8k = -5k - 5
To simplify the left side.
3
Add 8k8k to both sides of the equation.
13=3k−513 = 3k - 5
To gather all terms with the variable kk on the right side.
4
Add 55 to both sides of the equation.
18=3k18 = 3k
To isolate the variable term.
5
Divide both sides by 33.
k=6k = 6
To solve for kk.

Key Concept

Solving one-variable linear equations by applying the distributive property and combining like terms.
Rate this question

Topics

Solving One-Variable Linear Equations

More questions from this topic