Solving Linear Equations, all mixed up

EXAMPLES:

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

Solution:

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

Solve: $3 - 2x = 5x + 1$

Solution:

$3 - 2x = 5x + 1$	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

Solve: $\displaystyle -3x -\frac{8}{9} = \frac{5}{6}$

Solution:

$\displaystyle -3x -\frac{8}{9} = \frac{5}{6}$	original equation
$\displaystyle 18\left(-3x -\frac{8}{9}\right) = 18(\frac{5}{6})$	multiply both sides by $\,18\,$, which is the least common multiple of $\,9\,$ and $\,6\,$
$-54x - 16 = 15$	simplify; all fractions are gone
$-54x = 31$	add $\,16\,$ to both sides
$\displaystyle x = -\frac{31}{54}$	divide both sides by $\,-54\,$

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Simple Word Problems resulting in Linear Equations

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.