Vocabulary

Solution: A solution to an equation is the value of the variable that makes the statement true. 

Concept

Determine if the statement is true for problems where solutions are proposed for equations with variables on both sides of the form ax + b = cx + d where a, b, c & d are rational numbers.

Rules

1. Gather the variable terms together on one side of the equal sign by adding or subtracting.
2. Isolate the variable term by adding or subtracting the constant. 
3. Isolate the variable by multiplying or dividing by the coefficient.
4. If the two sides of the equation are NOT equal, then the given value is NOT a solution of the equation.

Example

Select whether the given statement is true or false. 

v = -8 is the solution for 18v + 3 = 34v + 13

Solution

Substitute (-8) for “v” to determine if v = -8 is a solution for 18v + 3 = 34v + 13

 18v + 3 = 34v + 13

 18(-8) + 3 = 34(-8) + 13

-1 + 3 = -6 + 13

2 ≠ 7

False. -8 is NOT a solution to the given equation.

Pre-requisite Skills

Solve Two-Step Equations (8.2.2)

Solve Complex Equations (7.6.5)