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Linear Equations and Inequalities

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.

  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.


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