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Question

Difficulty: MediumSolving One-Variable Linear Equations

Calculate the precise value of kk that makes the following algebraic equation true:

5(2k−3)=3k+13 5(2k - 3) = 3k + 13

Answer: 4

Answer

4
The correct value is found by distributing the 5, gathering all variable terms on one side and constants on the other, and finally dividing by the variable's coefficient.

Step-by-Step Solution

1
Apply the distributive property on the left side of the equation.
10k−15=3k+1310k - 15 = 3k + 13
To eliminate the parentheses and expose the variable terms for grouping.
2
Subtract 3k3k from both sides.
7k−15=137k - 15 = 13
To collect all terms containing the variable kk on one side of the equation.
3
Add 1515 to both sides.
7k=287k = 28
To isolate the variable term by moving constants to the opposite side.
4
Divide both sides by 77.
k=4k = 4
To solve for the final value of kk.

Key Concept

Solving linear equations with variables on both sides using the distributive property.
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Topics

Solving One-Variable Linear Equations

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