Download A mathematical sentence with an equal sign is an equation. An

January 3¸ 2012
2-1 SOLVING ONE-STEP EQUATIONS
Page 61
A mathematical sentence with an equal sign is an equation. An equation is like a
balance scale. If you do something to one side of an equation, you must do the
same to the other side to keep the equation balanced.
A solution to an equation is any value that makes the equation true. To find a
solution of an equation, isolate the variable, or get the variable alone on one side.
Use inverse operations, operations that undo each other to isolate a variable.
Example 1/ Solving Equations by Adding:
Solve -2 = k – 14.
-2 = k - 14
-2 + 14 = k - 14 + 14
12 = k
Since 14 is subtracted from k, you must add 14 to
each side to isolate k.
Add 14 to each side. This is where adding and
subtracting integers comes in to play.
Simplify.
Example 2/ Solving Equations by Subtracting:
Money - You add $35 to your bank account and the new balance is $243. Write and solve an
equation to find your previous balance.
Words
Equation
Previous balance plus deposit = new balance
b
+
35
= 243
b + 35 = 243
b + 35 – 35 = 243 - 35
b = 208
Since 35 is added to b, you must subtract 35 from
each side to isolate b.
Subtract 35 from each side. This is where adding and
subtracting integers comes in to play.
Simplify.
Your previous balance was $208.
January 3¸ 2012
Example 3/ Solving Equations by Multiplying:
Solve
= 15.
Since x is divided by -7, you must multiply each side by -7 to
isolate x.
= 15
-7 x (
Multiply each side by -7.
)= 15
X = -105
Simplify.
Example 4/ Solving Equations by Dividing:
Solve
.
Since c is multiplied by 8, you must divide each side by 8 to
isolate c.
=
102 = c
Divide each side by 8.
Simplify.