ALEKS YELLOW Solving a linear equation with several occurrences
of the variable: Problem type 1
Although this problem type has several occurrences of the variable, you will solve it the
same as you do any linear equation:
1.
2.
3.
4.
5.
Eliminate fractions
Distribute numbers through any parenthesis then combine like terms
Add or subtract to “move” all variables to the left then combine like terms
Add or subtract to “move” all variables to the right then combine like terms
Multiply or divide to isolate the variable
Here is an example: 3  x  8  8x  35
STEP ONE: Eliminate fractions
There are no fractions to eliminate in this problem
STEP TWO: Distribute …
3  x  8   8x  35
3x  3  8   8x  35
3x  24  8x  35
…then combine like terms
3x  24  8x  35
3x  24  8x  35
11x  24  35
STEP THREE: “Move” variables to the left then combine like terms
All terms with variables in them are already on the left
STEP FOUR: “Move” constants to the right …
11x  24  35
Add 24 to both sides:
11x  24  24  35  24
11x 24 24  35  24
11x  35  24
…then combine like terms
11x  35  24
11x  11
STEP FIVE: Divide by the coefficient of the variable to isolate the variable:
11x  11
11x
11

11
11
11 x

11
x  1
1
11
11