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Solve for x: 3x + 12 = 48 - x
8
9
10
12
9
Use the unit digit or quick transposition: add x to 3x to get 4x, and subtract 12 from 48 to get 36. Since 4x = 36, x must be 9.
A linear equation in one variable: 3x + 12 = 48 - x
ax+b=cтИТdx
Use the unit digit or quick transposition: add x to 3x to get 4x, and subtract 12 from 48 to get 36. Since 4x = 36, x must be 9.
Students often make a sign error when transposing -x to the left side, accidentally writing 2x instead of 4x.
Group like terms
Collect the variable terms on the left side and constant terms on the right side by adding x to both sides and subtracting 12 from both sides.
3x+x=48тИТ12
Simplify both sides
Perform the arithmetic operations to consolidate the variables and constants.
4x=36
Solve for x
Divide both sides by 4 to isolate x.
x=436тАЛ=9
B is correct because solving the equation 3x+12=48тИТx yields 4x=36, which results in x=9.
Mastering the movement of variables across the equal sign is the foundation for solving complex word problems, including Age, Time-Speed-Distance, and Profit-Loss equations.
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