Solving Simple Linear Equations with Integer Coefficients

You may want to review these two tools:

Examples

Solve: $\,x - 3 = 5\,$

Answer: $x = 8$

Note: Some of these equations are so simple that you may want to solve them by inspection. That is, just stop and think: What number, minus $\,3\,,$ gives $\,5\,$?

Solve: $\,2x = 5\,$

Answer: $x = \frac{5}{2}$

Note: You can input this answer as 2.5 or 5/2 . That is, you can input answers as fractions or decimals.

Solve: $\,2x - 1 = 5\,$

Answer: $x = 3$

Note: For some of the more complicated equations, you may want to use the Addition and Multiplication Properties of Equality.

$2x-1=5$	original equation
$2x=6$	add $\,1\,$ to both sides
$x = 3$	divide both sides by $\,2$

Practice

For more advanced students, a graph is available. For example, the equation $\,2x - 1 = 5\,$ is optionally accompanied by the graph of $\,y = 2x-1\,$ (the left side of the equation, dashed green) and the graph of $\,y = 5\,$ (the right side of the equation, solid purple).

Notice that you are finding the value of $\,x\,$ where these graphs intersect. Click the ‘Show/Hide Graph’ button to toggle the graph.