Education.com
Try
Brainzy
Try
Plus

Simplifying Expressions and Solving Equation Word Problems Study Guide (page 2)

based on 2 ratings
By
Updated on Oct 3, 2011

Solving Equations with Multiple Steps

One-Step Equations

One-step equations are named this because they have only one operation to undo, so they should take only one step to solve. Use inverse, or opposite, operations to get the variable alone. This is called isolating the variable.

    Example: Solve the equation for x.
3x = 12  
Divide each side by 3, the inverse operation of multiplying by 3.
x = 4 The variable is alone.

Two-Step Equations

Two-step equations have two operations, and therefore take two steps to solve.

    Example: Solve the equation for x.
– 10 = 10  
–10 + 10 = 10 + 10 Add 10 to each side, the inverse operation of subtracting 10.
= 20 Simplify.
× 4 = 20 × 4 Multiply each side by 4, the inverse operation of dividing by 4.
x = 80 The variable is alone.

Variables on Both Sides of the Equation

When there are variables on both sides of the equation, get rid of the variable with the smaller coefficient by using the inverse operation.

    Example: Solve the equation for x.
7x = 3x + 28  
7x – 3x = 3x – 3x + 28 Subtract 3x from each side of the equation.
4x = 28 Simplify.
Divide each side by 4, the inverse operation of multiplying by 4.
x = 7 The variable is alone.

Multistep Equations

To solve multistep equations, you may first need to use the distributive property and combine like terms in order to simplify. If there are variables on both sides of the equation, handle them next. Finally, use the inverse operations to isolate the variable in the one- or two-step equation.

    Example: Solve the equation for x.
2(x – 6) – x = 5x  
2x – 12 – x = 5x Get rid of the parentheses by using the distributive property.
x – 12 = 5x Combine like terms.
xx – 12 = 5xx Subtract x from each side of the equation.
–12 = 4x Simplify.
Divide each side by 4, the inverse operation of multiplying by 4.
–3 = x The variable is alone.

Tip:

The equation solving steps can be summarized as the following:

  1. Get rid of parentheses.
  2. Combine like terms.
  3. Handle variables of both sides of the equation.
  4. Solve the one- or two-step equation.

View Full Article
Add your own comment