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Difficulty: MediumSolving One-Variable Linear Equations

Consider the following algebraic equation:

5(2m−1)−3m=2(m+10) 5(2m - 1) - 3m = 2(m + 10)

What is the value of the variable mm?

Answer: 5

Answer

5
By correctly applying the distributive property on both sides of the equation, combining the resulting like terms, and applying algebraic operations to isolate the variable, the equation simplifies to 5m=255m = 25, which yields exactly 55.

Step-by-Step Solution

1
Distribute the constants outside the parentheses into the terms inside.
10m−5−3m=2m+2010m - 5 - 3m = 2m + 20
This removes the parentheses and allows us to combine like terms.
2
Combine the like variable terms on the left side (10m10m and −3m-3m).
7m−5=2m+207m - 5 = 2m + 20
Simplifying each side independently makes the equation easier to solve.
3
Subtract 2m2m from both sides and add 55 to both sides.
5m=255m = 25
This groups all variable terms on the left and all constant terms on the right.
4
Divide both sides by 55.
m=5m = 5
This isolates the variable mm to give the final solution.

Key Concept

Solving one-variable linear equations requiring distribution and combining like terms
Estimated Time:1m 0s
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Topics

Solving One-Variable Linear Equations

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