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Question

Difficulty: MediumSolving One-Variable Linear Equations

Solve for tt in the equation below:

3(2t−4)+5=5t−(t−9) 3(2t - 4) + 5 = 5t - (t - 9)
Answer:The value of tt is 【8】.

Answer

The correct value for tt is 8.
By properly distributing values into the parentheses, combining like terms, and isolating the variable using inverse operations, the equation simplifies to 2t=162t = 16, which yields t=8t = 8.

Step-by-Step Solution

1
Distribute the 3 into the parentheses on the left side, and distribute the negative sign into the parentheses on the right side.
6t−12+5=5t−t+96t - 12 + 5 = 5t - t + 9
To eliminate the parentheses so that all terms can be properly combined.
2
Combine the constant terms on the left side and the like variable terms on the right side.
6t−7=4t+96t - 7 = 4t + 9
To simplify both sides of the equation independently before moving terms across the equals sign.
3
Subtract 4t4t from both sides of the equation.
2t−7=92t - 7 = 9
To gather all the variable terms onto the left side.
4
Add 7 to both sides of the equation.
2t=162t = 16
To isolate the term containing the variable.
5
Divide both sides by 2.
t=8t = 8
To find the final numerical value of tt.

Key Concept

Solving One-Variable Linear Equations
Estimated Time:1m 30s
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Topics

Solving One-Variable Linear Equations

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