1.
1-step Equations: + and – 9/23/13
In elementary school, you solved
equations that looked like this:
In Algebra, we just use a variable
instead of the box!
We could rewrite the same
equation like this: x + 3 = 5
2.
To solve:
Need to get x by itself.
We must “undo” whatever has been
done to the variable.
Do the same to BOTH SIDES of the =
sign!
Answer should be: x = some number.
3.
Equations Have to Balance!
Both sides of the = sign must “weigh”
the same!
When you change one side, do the
same to the other side, so it stays
balanced!
x + 3 = 7
4.
Examples:
Solve each equation. Check your
answers!
x + 3 = -7 m – 6 = 8
7.
You Try!
Solve each equation. Check your
answers!
x – 9 = -6 1.6 + n = 10.7
8.
1-step Equations: × and ÷ 9/24/13
Just like with adding and
subtracting, we need to “undo” what is
done to x.
Use division to “undo” multiplication.
Use multiplication to “undo” division.
Remember: A fraction bar means
divide!
Example: says x divided by 3!
10.
You Try!
Solve each 1-step equation.
-4.2a = 16.6
11.
Applications 9/26/13
How to solve a word problem using a
linear equation:
1. Write a verbal model
2. Define a variable for the unknown
3. Write an equation
4. Solve
5. Answer the question in sentence form
12.
Common Language:
In a word problem:
“is” means =
“of” means multiply
“per” means multiply
“less than” usually means subtract
“more than” usually means add
13.
Example 1
Paula has 3 more dolls than her friend
Briana. If Paula has 10 dolls, write and
solve an equation to find out how many
dolls Briana has.
Let be
Paula’s
dolls
Briana’s
dolls
+ 3=
Briana’s dollsb
10 = b + 3
14.
You Try!
A used book costs $17 less than the
same book new. The used book costs
$9. Write and solve an equation to
find out how much the new book cost.
15.
Example 2
The melting point of bromine is of the
melting point of nitrogen. The melting point
of bromine is −7 C. Write and solve an
equation to ﬁnd the melting point of
nitrogen.
Let be the
Melting
point of
bromine
1/30
Melting
point of
nitrogen
=
Melting point of nitrogenn
-7 = 1/30 n
16.
You Try!
The melting point of mercury is about
of the melting point of krypton. The
melting point of mercury is −39 C. Write
and solve an equation to ﬁnd the melting
point of krypton.
17.
Example 3
John earns $5 per hour mowing
lawns. Write and solve an equation to
find how many hours he must work to
earn $40.
Let be the
Amount
earned $5
# of
hours=
# of hoursh
40 = 5 h
18.
You Try!
If you save at a rate of $15 per month,
how long will it take you to save $135?
Write and solve an equation.
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