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Find the value of x if 3x + 5 = 20 - 2x.
3
5
4
2
3
Mentally group like terms by adding 2x to 3x to get 5x, and subtracting 5 from 20 to get 15, yielding x=3 instantly.
Linear equation: 3x + 5 = 20 - 2x
3x+5=20тИТ2x
Mentally group like terms by adding 2x to 3x to get 5x, and subtracting 5 from 20 to get 15, yielding x=3 instantly.
Making a sign error while transposing тИТ2x or +5 across the equals sign.
Write the Given Equation
Start with the given linear equation in one variable: 3x+5=20тИТ2x.
3x+5=20тИТ2x
Group Variable Terms
Transpose the тИТ2x term from the right-hand side to the left-hand side by changing its sign: 3x+2x+5=20.
3x+2x+5=20
Group Constant Terms
Transpose the +5 term from the left-hand side to the right-hand side: 5x=20тИТ5.
5x=20тИТ5
Solve for x
Simplify both sides to get 5x=15, then divide by 5 to isolate x.
x=515тАЛ=3
A is correct because solving the equation gives x=3.
Linear equations form the foundation for solving simultaneous equations, ratio-proportion problems, and word problems in quantitative aptitude.
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