Mathematics » Solving Linear Equations I » Solve Equations Using the Subtraction and Addition Properties of Equality

# Solving Equations That Need to Be Simplified

## Solving Equations That Need to Be Simplified

In the examples up to this point, we have been able to isolate the variable with just one operation. Many of the equations we encounter in algebra will take more steps to solve. Usually, we will need to simplify one or both sides of an equation before using the Subtraction or Addition Properties of Equality. You should always simplify as much as possible before trying to isolate the variable.

## Example

Solve: $$3x-7-2x-4=1.$$

### Solution

The left side of the equation has an expression that we should simplify before trying to isolate the variable.  Rearrange the terms, using the Commutative Property of Addition.  Combine like terms.  Add 11 to both sides to isolate $$x$$.  Simplify.  Check. Substitute $$x=12$$ into the original equation.  The solution checks.

## Example

Solve: $$3\left(n-4\right)-2n=-3.$$

### Solution

The left side of the equation has an expression that we should simplify.  Distribute on the left.  Use the Commutative Property to rearrange terms.  Combine like terms.  Isolate n using the Addition Property of Equality.  Simplify.  Check. Substitute $$n=9$$ into the original equation.  The solution checks.

## Example

Solve: $$2\left(3k-1\right)-5k=-2-7.$$

### Solution

Both sides of the equation have expressions that we should simplify before we isolate the variable.  Distribute on the left, subtract on the right.  Use the Commutative Property of Addition.  Combine like terms.  Undo subtraction by using the Addition Property of Equality.  Simplify.  Check. Let $$k=-7.$$  The solution checks.