Equation-Solving Main Menu

LINEAR EQUATIONS

A linear equation is one that can be expressed in the form: 

Linear equations are also called first degree equations because a linear equation consists of polynomial expressions in which the highest degreed term is one.

EXAMPLES OF LINEAR EQUATIONS

Example 1

Example 2

2(x - 4) + 5x = -22

STEPS TO SOLVE A LINEAR EQUATION

1. Clear fractions by multiplying all terms by the lowest common denominator.
2. Simplify the algebraic expression on each side.
   • remove parentheses using the distributive property
   • Combine all like terms
3. Collect all the variable terms to one side and all the constant terms to the other side.
   • add/subtract variable terms to both sides of the equation
   • add/subtract constant terms to both sides of the equation
4. Divide both sides of the equation by the coefficient of the variable.
5. Check the answer in the original equation.

Sample Problems

Sample Problem 1

2(x - 4) + 5x = - 22

2x - 8 + 5x = - 22

7x - 8 = - 22
    + 8     + 8

7x = - 14

x = - 2

CHECK:  2(x - 4) + 5x = - 22

2(-2 - 4) + 5(-2)  = - 22 (?)

2(-6) + 5(- 2) = - 22

-12 - 10 = - 22

-22 = - 22  ü

Combine like terms

Isolate the variable to one side. Here, add 8 to both sides.

Divide both sides by the coefficient of the variable.

This is the proposed solution. Now check in the original equation to verify.
CHECK:
Replace the solution in for the variable where ever the variable appears.

Work each side of the separately using the order of operations.

Both sides must be the same.

Sample Problems

Sample Problem 2

5(3x) = 2x - 78

15x = 2x - 78
 -2x   -2x         

13x = - 78

13x = - 78
13        13

x = - 6

CHECK

ü

 
Simplify each side

Isolate the variable to one side

Divide both sides by 13

The proposed solution is 6.

CHECK

Replace the solution in for the variable where ever the variable appears.

Work each side of the separately using the order of operations.

Both sides must be the same.