Transcript Solving Equations with Addition and Subtraction

Warm Up
You need your calculator and acti-vote
1. -3(4x – 8) +7(-4 + 3x)
2. -4(2n + 3) – 2(1 + 2n)
HW Solutions
2.
3.
4.
5.
6.
7.
8.
9.
21x + 22
20x + 29
3x + 36
29x + 6
25x + 42
13x + 30
42x + 46
20x + 53
10.
11.
12.
13.
14.
15.
16.
17.
18.
12m + 22
13m + 49
10m + 10
15m + 35
23m + 33
19m + 54
43m + 24
39m + 73
66m + 18
Objective
The student will be able to:
solve equations using addition and
subtraction.
solve equations using multiplication
and division.
1) Solve r + 16 = -7
Think of this equation as a balance scale.
Whatever you do to one side has to be done to the
other to keep it balanced!
1) Solve r + 16 = -7
To solve, you must get the variable by
itself.
What number is on the same side as r?
16
To get r by itself, we must undo the
“add 16”. What is the opposite of
addition?
Subtract 16
1.
2.
3.
4.
1) Solve r + 16 = -7
Draw “the river” to
16
-16
separate the equation
into 2 sides
r
=
-23
Subtract 16 from both
sides
Simplify vertically
Check your answer
by substituting your
answer back into the
problem
-23 + 16 = -7
2) Solve x + 2 = -3
Get the variable by itself. What is your
first step?
1.
2.
3.
4.
Add 2 to both sides
Subtract 2 from both sides
Add 3 to both sides
Subtract 3 from both sides
Answer Now
1.
2.
3.
4.
2) Solve x + 2 = -3
Draw “the river” to
2
2
separate the equation
into 2 sides
x
=
-5
Subtract 2 from both
sides
Simplify vertically
Check your answer
by substituting your
answer back into the
problem
-5 + 2 = -3
On homework and tests, be sure to check your work!!
There is no reason why you should miss a problem!
3) Solve 8 = m - 3
1.
2.
3.
4.
m=5
m = 11
m = 24
m = 8/3
Answer Now
1.
2.
3.
4.
3) Solve 8 = m - 3
Draw “the river” to
+
3
+
3
separate the equation
into 2 sides
11=
m
Add 3 to both sides
Simplify vertically
Check your answer
by substituting your
answer back into the
problem
8 = 11 - 3
When solving equations, we want to
eliminate double signs.
y + (-3) = 8
is rewritten as
y–3=8
p – (-5) = 6
is rewritten as
p+5=6
As a general rule, replace “+ (- )” with “–” and “– (- )” with “+”.
This will make things less confusing in the future!
4) Solve y + (-3) = 7
1.
2.
3.
4.
5.
Draw “the river” to
separate the equation
into 2 sides
Eliminate the double
sign
Add 3 to both sides
Simplify vertically
Check your answer
by substituting your
answer back into the
problem
y–3 =7
+ 3 +3
y
= 10
10 + (-3) = 7
5) Solve. -x - (-2) = 1
1.
2.
3.
4.
5.
6.
Draw “the river” to
separate the equation into
2 sides
Eliminate the double sign
Subtract 2 from both sides
Simplify vertically
We haven’t gotten x by
itself. If we read this
aloud, it is “the opposite
of x equals -1”. What
would x be equal?
Check your answer
-x + 2 = 1
-2 -2
-x
= -1
x
= 1
-(1) + 2 = 1
Solve -y – (-3) = 7
1.
2.
3.
4.
y = 10
y=4
y = -10
y = -4
Answer Now
6) Solve. -5t = 60
To get the variable by itself, which
number needs to be moved?
-5
To move the -5, you have to do the
opposite operation. What operation
will we use?
division
1.
6) Solve -5t = 60
-5 -5
Draw “the river” to
t = -12
separate the equation
into 2 sides
2. Divide both sides by -5
3. Simplify
4. Check your answer
-5(-12) = 60
7) Solve 15 = 6n
6
6
1. Draw “the river”
2. Divide both sides by 6
2.5 = n
4.
3. Simplify
Check your answer
15 = 6(2.5)
8) Solve -3v = -129
1.
2.
3.
4.
v = -126
v = -43
v = 43
v = 126
Answer Now
x
 12
9) Solve
4
You don’t like fractions? Let’s get rid of
them! 
“Clear the fraction”
by multiplying both sides of the equation
by the denominator.
x
9) Solve  12
4
1. Draw “the river”
x
2. Clear the fraction –
4 ·  12 · 4
multiply both sides by 4
4
4.
3. Simplify
Check your answer
x = -48
48
 12
4
2x
10) Solve
= 18
3
2x
3·
= 18 · 3
Draw “the river”
3
Clear the fraction –
1.
2.
multiply both sides by 3
3. Simplify
4. Divide both sides by 2
5. Simplify
6. Check your answer
2x = 54
2
2
x = 27
2(27)
 18
3
11) Which step clears the fraction in
3b
 12
5
1.
2.
3.
4.
Multiply by 3
Multiply by 5
Multiply by -12
Multiply by -5
Answer Now
4b
 8
12) Solve
7
1.
2.
3.
4.
b = -56
b = -14
b = 14
b = 56
Answer Now
Example 13
Katie is twice as old as her sister Mara. The
sum of their ages is 24. How old is each
sister?
Example 14
Twenty-one subtracted from a number is -8.
Find the number