A mathematical statement that contains an equal sign is called
an equation .
Steps for Solving Equations:
1. Remove parentheses by multiplying (this step is not always
necessary)
2. Collect like terms on each side of the equal sign
3. Isolate the variable by undoing the operation
4. Check by substituting the solution into the original
equation
The equal sign divides equations into 2 parts or 2 sides.
Equations are like balance scales. Whatever is done to one side,
must be done to the other side in order to maintain equality or
balance.
Example 1
z + 6 = -9
There are no parentheses to be removed
and no likes terms to collect
z + 6 - 6 = -9 - 6
To isolate the variable, we
"undo" the +6 by subtracting 6 from each side
z = -15
Check:
substitute -15 for z in the original equation
(-15) + 6 = -9
-9 = -9
Example 2
x - (-4) = 10
There are no parentheses to be removed
and no likes terms to collect
x + 4 = 10
Since there are 2 negative signs, we
"add the opposite" to avoid confusion
x + 4 -4 = 10 -4
To isolate the variable, we
"undo" the +4 by subtracting 4 from each side
x = 6
Check:
substitute 6 for x in the original equation
6 - (-4) = 10 (remember to "add the opposite")
10 = 10
Example 3
p - (-2) = -2
There are no parentheses to be removed
and no likes terms to collect
p + 2 = -2
Since there are 2 negative signs, we add
the opposite to avoid confusion
p + 2 -2 = -2 -2
To isolate the variable, we undo the +2
by subtracting 2 from each side
p = -4
Check:
substitute -4 for p in the original equation
(-4) - (-2) = -2 (remember to add the opposite)
-4 + 2 = -2
-2 = -2
Example 4
x + (-21) = 5.3
There are no parentheses to be removed
and no likes terms to collect
x + (-21) + 2.1 = 5.3 + 2.1
To isolate the variable, we
"undo" the -2.1 by adding 2.1 to each side
x = 7.4
Check:
substitute 7.4 for x in the original equation (7.4) + (-2.1) =
5.3
5.3 = 5.3
Buy
Algebrator now:
Instant download and
optional CD
Only $39.99
Click to Buy Now:
Attention: We are
currently running a special promotional offer
for equation-solver.com Visitors -- if you order
Algebrator by midnight of
July 4th
you will pay only $39.99
instead of our regular price of $74.99 -- this is $35.00 in
savings ! In order to take advantage of this
offer, you need to order by clicking on one of
the buttons on the left, not through our regular
order page.
If you order now you will also receive 30 minutes of live math tutoring from tutor.com!
You
Will Learn Algebra Better - Guaranteed!
Just
take a look how incredibly simple Algebrator is:
Step 1
: Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:
Step 2 :
Let Algebrator solve it:
Step 3 : Ask for an explanation for the steps you don't understand:
Algebrator can solve problems in all the following areas:
simplification of algebraic expressions (operations
with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots
(radicals), absolute values)
factoring and expanding expressions
finding LCM and GCF
operations with complex numbers
(simplifying, rationalizing complex denominators...)
solving linear, quadratic and many other equations
and inequalities
(including basic logarithmic and exponential equations)
solving a system of two and three linear equations
(including Cramer's rule)
