5.07 PowerPoint Review
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Transcript 5.07 PowerPoint Review
SOLVING INEQUALITIES
x 5 9
Step 1: Subtract 5 from both sides
x 5 5 9 5
Step 2: Make a Clean Sweep
x 5 5 9 5
+5 – 5 equals 0, leaving
“x” all by itself=)
x 14
Since -9 and -5 have the
same sign, add their
absolute values.
9 5 14
Since the numbers are both
negative, the answer is
negative.
14
Final Answer
SOLVING INEQUALITIES
5 x 6
Step 1: Divide both sides by -5
5 x
6
5
5
Divide by -5 because: -5 and x are involved in
multiplying… The opposite of multiplying is dividing
Step 2: Make sure to change
inequality sign
5x
6
5
5
Change inequality sign
whenever
MULTIPLYING OR
DIVIDING by a
NEGATIVE number=)
Step 3: Make a Clean Sweep
5x 6
When dividing a
5
5
The -5’s divide out,
leaving “x” by itself.
negative number by a
negative number, the
answer is positive.
Final Answer1
x 1.2 or x 1
5
SOLVING INEQUALITIES
b
7
4
Step 1: Multiply both sides by 7
7
b
7
4 7
Multiply both sides by 7
because: 7 and b are involved
in division… The opposite of
dividing is multiplying.
Step 2: Make a Clean Sweep
7
b
7
4 7
The 7’s divide out,
leaving “x” by itself.
b 28
A negative times a positive
equals a negative so -4
times 7 is -28.
Final Answer
SOLVING INEQUALITIES
w
4
8
Step 1: Multiply both sides by -4
4
w
4
8 4
Multiply both sides by – 4 because: -4 and w
are involved in division… The opposite of
dividing is multiplying
Step 2: Make sure to change
inequality sign
4
w
4
8 4
Change inequality sign
whenever
MULTIPLYING OR
DIVIDING by a
NEGATIVE number=)
Step 3: Make a Clean Sweep
4
w
4
8 4
The -4’s divide out,
leaving “x” by itself.
A positive times a
negative equals a
negative.
8 times -4 is -32.
b 32
Final Answer
SOLVING INEQUALITIES
4c 2 30
Step 1: Subtract 2 from both sides
4c 2 2 30 2
4c 2 2 30 2
+2 -2 =0, leaving “4c” by
itself.
Perform adding and
subtracting first
when solving 2-step
inequalities=)
30 – 2 = 28
4c 28
Subtract 2 from both sides because: 2 is involved addition and
the opposite of adding is subtracting=)
Step 2: Divide both sides by 4 Divide by 4 because: 4 and c are
4c 28
4
4
involved in multiplying… The opposite
of multiplying is dividing
Step 3: Make a Clean Sweep
4c 28
4
4
The 4’s divide out,
leaving “c” by itself.
c 7
28 divided by 4
equals 7.
Final
Answer
SOLVING INEQUALITIES
3d 9 12
Step 1: Add 9 to both sides
3d 9 9 12 9
3d 9 9 12 9
-9 +9 =0, leaving “-3d” by
itself.
Perform adding and
subtracting first
when solving 2-step
inequalities=)
12 + 9 = 21
3d 21
Add 9 to both sides because: 9 is involved subtraction
and the opposite of subtracting is adding=)
Step 2: Divide both sides by -3
3d 21
3
3
Divide by -3 because: -3 and d
are involved in multiplying…
The opposite of multiplying is
dividing
Change inequality sign
whenever
MULTIPLYING OR
DIVIDING by a
NEGATIVE number=)
Step 3: Make a Clean Sweep
3d 21
3
3
A positive divided by a
negative equals a negative
21 divided by -3 equals -7.
The -3’s divide out,
leaving “d” by itself.
d 7
Final
Answer
SOLVING INEQUALITIES
3y 7y 1 31
Step 1: Combine Like Terms
3y 7y 1 31
3y and -7y are like terms.
Since 3y and -7y have
The answer keeps the sign of the
opposite signs, we subtract integer with the larger absolute
the coefficients. (3 and -7 value
are the coefficients)
4 y 1 31
3 7 4
Add 1 to both sides because: 1 is
Step 2: Add 1 to Both Sides involved subtraction and the opposite
of subtracting is adding=)
4y 1 31
4y 1 1 31 1
31 + 1 =32
-1 +1 =0, leaving “-4y” by itself.
4y 32
Step 3:Divide by 4 & Make a Clean Sweep
4y 32
4
4
We change inequality
sign whenever we
MULTIPLY OR DIVIDE by
a NEGATIVE number=)
A positive divided by a
negative equals a negative.
32 divided by -4 equals -8.
The -4’s divide out,
leaving “y” by itself.
y 8
Final Answer
SOLVING INEQUALITIES
8a 2a 9 1
Step 1: Combine Like Terms
8a 2a 9 1
9 and 1 are both integers so
we add them. 9 + 1 =10
8a and 2a are like terms so we
add the coefficients. 8 + 2 =10
10a 10
Step 2: Divide both sides by 10
10a 10
10 10
Divide by 10 because: 10 and a are involved
in multiplying… The opposite of multiplying is
dividing
Step 3: Make a Clean Sweep
10a 10
10 10
The 10’s divide out,
leaving “a” by itself.
10 divided by 10
equals 1.
a 1
Final Answer
SOLVING INEQUALITIES
x
2 7
6
Perform adding and
subtracting first
when solving 2-step
inequalities=)
Step 1: Subtract 2 from both sides
x
2 2 7 2
6
Since -7 and -2 have the same
+2 - 2 =0, leaving “x/6” sign, add their absolute values.
by itself.
72 9
x
6
9
Since the numbers are both
negative, the answer is negative.
Step 2: Multiply both sides by 6
6
x
6
9 6
9
Multiply by 6 because: 6 and x are
involved in dividing… The opposite of
dividing is multiplying
Step 3: Make a Clean Sweep
6
x
6
9 6
6 divided by 6 is 1.
A negative times a
positive equals a
negative.
-9 times 6 = -54
x 54
1x=x
Final Answer
SOLVING INEQUALITIES
x
4
5 5
Step 1: Add 5 to both sides
x
55 55
4
5 + 5 = 10
-5 + 5 =0, leaving “x/-4”
by itself.
x
4
10
Step 2: Multiply both sides by -4
4
x
4
10 4
Step 3: Make a Clean Sweep
4
x
4
10 4
4 divided by 4 is 1.
1x=x
Perform adding and
subtracting first
when solving 2-step
inequalities=)
A positive times a
negative equals a
negative.
10 times -4 = -40
Multiply by -4 because: -4 and x are
involved in dividing… The opposite
of dividing is multiplying
We change inequality
sign whenever we
MULTIPLY OR DIVIDE by
a NEGATIVE number=)
x 40
Final Answer
SOLVING INEQUALITIES
(b 5) 15
Step 1: Distribute the negative sign to each term inside the
parenthesis.
1(b 5) 15
Another way
1(b ) (1)(5) 15
to write the
negative sign
1b 5 15
is as a -1=)
Step 2: Subtract 5 from both sides.
1b 5 5 15 5
+5 - 5 =0, leaving
“-1b” by itself.
1b 10
Step 3: Divide both Sides by -1
1b 10
1
1
15 - 5 = 10
We change inequality
sign whenever we
MULTIPLY OR DIVIDE by
a NEGATIVE number=)
Step 4: Make a Clean Sweep
A positive divided by a
1b 10
negative equals a negative.
1
1
10 divided by -1 equals -10
The -1’s divide out,
leaving “b” by itself.
b 10
Final Answer