One method for solving a linear equation that looks like
is to simply guess
and check. What value can I substitute in for x so that the result will be 13?
After some
thought it should be easy to see that x must equal 5 here because
.
Linear Equation – An equation with one
variable where the exponent is not greater than 1. |
When solving, the idea is to isolate the variable by
applying the opposite operations to
both sides to retain the equality. In other words, if you add 5 to one side you
must add 5
to the other side as well.
Solve: | ||
The first opposite operation is to add 5 to both sides. |
||
Then to isolate the variable divide by 2. |
Tip: You can always check to see if your solution
is correct by substituting it in to the
original equation to see if it works. On a test, if you have time, you should
always check.
A.
Is a solution to ? |
Is a solution to ? |
Is a solution to |
B. Solve for x
Multiply or divide by -1 here. |
Multiplication is the opposite of division here. |
|
C. Solve for x
In Algebra, improper fractions are more natural to work with. |
Maria scored 7 more points than Jose on the first
mathematics exam. If Maria’s total score was 95 what was Jose’s total. (Set up an algebraic equation and solve it) |
Tip: Often it is handy to multiply both sides by
the reciprocal of the variable coefficient.
This technique can save a step or two by using the property
.
Multiply both sides by the reciprocal.. |
The order of operations is reversed when solving. Do the
addition and subtraction first
then multiply or divide as needed.
D. Solve for x