SOLVING MORE COMPLICATED
LINEAR EQUATIONS WITH INTEGER COEFFICIENTS
EXAMPLE:
Solve: $3 - 2x = 5x + 1$
Solution: Write a nice clean list of equivalent equations:
$3 - 2x = 5x + 1$ (original equation)
$3 = 7x + 1$ (add $\,2x\,$ to both sides)
$2 = 7x$ (subtract $\,1\,$ from both sides)
$\frac{2}{7} = x$ (divide both sides by $\,7\,$)
$x = \frac{2}{7}$ (write in the most conventional way)
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Solving Linear Equations Involving Fractions

 
 

For more advanced students, a graph is displayed.
For example, the equation $\,3 - 2x = 5x + 1\,$
is optionally accompanied by the graph of $\,y = 3 - 2x\,$ (the left side of the equation, dashed green)
and the graph of $\,y = 5x + 1\,$ (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 if you prefer not to see the graph.

Solve: