Solving More Complicated Linear Equations with Integer Coefficients

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Solving Simple 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.