A General Rule for Solving Equations

The following steps provide a good method to use when solving linear equations.

  1. Simplify each side of the equation by removing parentheses and combining like terms.
  2. Use addition or subtraction to isolate the variable term on one side of the equation.
  3. Use multiplication or division to solve for the variable.

Note: Fractions may be removed by multiplying each side of the equation by the common denominator.

Example:

Solve for z: 7z – (3z – 4) = 12

Solution:

Step 1. Simplify the left side of the equation by removing parentheses and combining like terms.

Distribute through by -1.

7z 3z+ 4 = 12

Combine like terms on the left side of the equation.

4z + 4 = 12

Step 2. Use subtraction to isolate the variable term on the left side of the equation.

Subtract 4 from each side of the equation.

4z + 4 – 4 = 12 – 4

4z = 8

Step 3. Use division to solve for the variable.

Divide each side of the equation by 4.

\frac{4z}{4} = \frac{8}{4}

The solution to 7z – (3z – 4) = 12 is z = 2.

Solve for y: (y - 11) - (y + 8) = 6y
Solve for x: 0.8(5x + 15) = 2.6 - (x + 3)