Download 3.1-One-Step-Equations

Solving One Step Equations
Solving One Step Equations
Equation – A mathematical sentence that contains the equal sign.
Expression – It is a combination of numbers, variables, and mathematical operations (no equal
signs).
(With expressions you follow the order of operations to solve it, but with equations you follow
the reverse order of operations to solve it.)
If you understand how to read an equation, then solving equations is easy. There are a few different
ways of solving equations; however, the following will focus on just a couple of ways.
Method 1 : Working backwards (only works on equations that have the variable on one side of the
equal sign). You read the equation as you would work it out, then you reverse the problem using the
inverse operations as you solve the problem to find the variable.
Method 2 : Isolating the variable: You move numbers or other variables to one side of the equal sign
so that only the variable you are solving for is on the other side of the equal sign all by itself. To
move things in an equation you do the same thing to both sides of the equation to keep it balanced.
An equation is like a balance scale where each amount of both sides of the equal sign weigh or are of
equal value to each other.
The following are examples of solving equations. It starts with simple one step equations (1), two
step equations (2), multiple step equations (3), variables on both sides of the equation (4), and solve
formulas for a specific variable (5).
[A variable (letter) stands for a number. When reading the variable simply refer to it as “some
number”.]
One Step Equations
Ex 1(a): n + 8 = 12
Some number plus eight equals twelve.
Method 1: Since you are add eight to some number to get twelve, you take 12 which is the final result
and subtract (the inverse operation to addition) 8 to get the variable n. Thus n = 4. [12 – 8 = 4].
Method 2: n + 8 = 12
-8 -8
n = 4
You subtract 8 from both sides of the equation to isolate the variable.
(Notice that the 8 on the left side of the equation disappears leaving just
the variable.) Thus the answer is the variable n equals 4.
Ex 1(b): m – 17 = 15
Some number minus seventeen equals fifteen.
Method 1: Since you are subtracting 17 from some number to get 15, you take 15 which is the final
result and add (the inverse operation to subtraction) 17 to get the variable.[15 +17 = 32] Thus m = 32.
Method 2: m – 17 = 15
You add 17 to both sides of the equation to get rid of the 17 on the left
side
+17 +17
of the equation and isolate the variable. (Notice that the 17 on the
left side
m
= 32
of the equation disappears leaving you with just the variable. Thus
m = 32.
Ex 1(c): -3p = 48
Negative three times some number equals forty-eight.
Method 1: Since you are multiplying –3 and some number to get 48, you take 48 which is the final
result and divide it by –3 to get the variable (p). [ 48  (-3) = -16] Thus p = -16.
Method 2: -3p = 48
You divide both sides of the equation by –3 to isolate the variable. Notice
(-3) (-3)
that the –3 on the left side of the equation disappears leaving you with just
p = -16
the variable. Thus p = -16 is the answer.
-3p = 48
You can also show work this way. Instead of using a division
symbol
-3
-3
you can show division by making fractions.
p = -16
Ex 1(d): n/5 = -20
Some number divided by five equals negative twenty.
Method 1: Since you are dividing some number by 5 to get –20, you take –20 which is the final result
and multiply (inverse operation) it by 5 to get the variable (n). Thus the result is n = -100.[5x(-20) =100]
Method 2: n/5 = -20
x5
x5
n = -100
You multiply both sides of the equation by 5 to isolate the variable.
Notice that (5/1) x (n/5) = n, so the 5 disappears on the left leaving
you with just the variable (n).
Keep in mind that sometimes you may want to re-write an equation to make the problem easier to see
how to solve it. You can use your properties and rules for integers to re-write equations. I find it
helpful to get my variable on the far left of the equation since I read from left to right. Take the first
four examples to see other ways of re-writing the equations.
n + 8 = 12
x – 17 = 15
-3y = 48
n/5 = -20
8 + n = 12
(-17) + x = 15
y(-3) = 48
(1/5)n = -20
Examples:
1. Simplify:
2. Simplify: n− 4 = 11
3. Simplify:
4. Simplify:
5. Simplify:
6. Simplify:
7. Simplify: x + 4.7 = −9.2
8. Simplify:
12 – n = 8
15 – x = -17
48  y = -3
n  (-20) = 5
12 – 8 = n
15 – (-17) = x
48  (-3) = y
n = (-20) x 5