Question

13x+7=8x+27

2x-1=7x+44

Answer 1

• x = 4
• x = -9

Explanation:

1. Locate the x-term with the smallest coefficient. Identify the constant on the other side of the equation. Subtract the sum of those values from both sides of the equation:

13x +7 -(7+8x) = 8x +27 -(7+8x)

5x = 20 . . . . simplify

x = 4 . . . . . . . divide by the coefficient of x

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2. Same procedure:

2x -1 -(2x+44) = 7x +44 -(2x+44)

-45 = 5x . . . . . . simplify

-9 = x . . . . . . . . . divide by the coefficient of x

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Comment on this type of problem

This sort of equation with constants and variables on both sides is called a 3-step linear equation, because it usually takes 3 steps to solve it:

1. collect the variables to one side
2. isolate the variable by subtracting the constant
3. divide by the coefficient of the variable.

In the above procedure, we have combined the first two steps. By locating and subtracting the variable term with the smallest coefficient, we ensure that the equation will have a positive coefficient for the variable. This can help reduce mistakes.