- Topics At a Glance
- Solutions to Equations
- Checking Solutions to Equations
- Number of Solutions to an Equation
- Equivalent Equations
- Solving Equations with One Variable
- Adding and Subtracting Constants
- Checking Answers
- Adding and Subtracting Variables
- Multiplication and Division
**Complicated Equations****Simplifying Equations**- Eliminating Fractions
- Keeping Both Solutions
- When You Get Stuck
- Solving Equations with Multiple Variables
- Solving Equations for Expressions
- Keeping Answers Pretty
- Factoring
- Geometry
- Single-Variable Inequalities
- Strict Inequalities
- Equivalent Inequalities
- Inequalities that Allow Equality
- Solving Inequalities
- In the Real World
- Fitting Things in Spaces
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

Sometimes parentheses make equations look more complicated than they actually are. (See how much more complicated this sentence seems?) If you simplify the expressions on each side of the equation before solving it, your life will be much easier.

Solve the equation 9(*x* - 2) + 3 = 5(1 - *x*).

First, simplify each side to find the equivalent equation:

9*x* - 15 = 5 - 5*x*

This looks much better. We solve this equation as usual:

Example 1

Solve the equation 4(1 - |

Exercise 1

Solve the equation 7*y* = -21.

Exercise 2

Solve the equation *z* + 2*z* - 3 = 4(*z* - 1).

Exercise 3

Solve the equation 3(*y* + 1) - 2(4 - 2*y*) = *y.*

Exercise 4

Solve the equation 0.5*x* - 2 + 0.25 = 0.25(*x* - 2).

Exercise 5

Solve the equation 3(1 -* x*) - 2(5 - 5*x*) = 2*x* + 3(1 + 5).