1. SOLVING INEQUALITIES Final Answer Step 1: Subtract 5 from both sides
Step 2: Make a Clean Sweep
Since -9 and -5 have the same sign, add their absolute values.
+5 – 5 equals 0, leaving “x” all by itself=)
Since the numbers are both negative, the answer is negative.
Final Answer

2. SOLVING INEQUALITIES Final Answer Step 1: Divide both sides by -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
Change inequality sign whenever MULTIPLYING OR DIVIDING by a NEGATIVE number=)
Step 3: Make a Clean Sweep
When dividing a negative number by a negative number, the answer is positive.
The -5’s divide out, leaving “x” by itself.
Final Answer

3. The 7’s divide out, leaving “x” by itself.
SOLVING INEQUALITIES
Multiply both sides by 7 because: 7 and b are involved in division… The opposite of dividing is multiplying.
Step 1: Multiply both sides by 7
Step 2: Make a Clean Sweep
A negative times a positive equals a negative so -4 times 7 is -28.
The 7’s divide out, leaving “x” by itself.
Final Answer

4. The -4’s divide out, leaving “x” by itself.
SOLVING INEQUALITIES
Step 1: Multiply both sides by -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
Change inequality sign whenever MULTIPLYING OR DIVIDING by a NEGATIVE number=)
Step 3: Make a Clean Sweep
A positive times a negative equals a negative.
8 times -4 is -32.
The -4’s divide out, leaving “x” by itself.
Final Answer

5. SOLVING INEQUALITIES Final Answer Step 1: Subtract 2 from both sides
Perform adding and subtracting first when solving 2-step inequalities=)
+2 -2 =0, leaving “4c” by itself.
30 – 2 = 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 involved in multiplying… The opposite of multiplying is dividing
Step 3: Make a Clean Sweep
28 divided by 4 equals 7.
Final Answer
The 4’s divide out, leaving “c” by itself.

6. SOLVING INEQUALITIES Final Answer Step 1: Add 9 to both sides
Perform adding and subtracting first when solving 2-step inequalities=)
-9 +9 =0, leaving “-3d” by itself.
= 21
Add 9 to both sides because: 9 is involved subtraction and the opposite of subtracting is adding=)
Change inequality sign whenever MULTIPLYING OR DIVIDING by a NEGATIVE number=)
Step 2: Divide both sides by -3
Divide by -3 because: -3 and d are involved in multiplying… The opposite of multiplying is dividing
Step 3: Make a Clean Sweep
A positive divided by a negative equals a negative
21 divided by -3 equals -7.
Final Answer
The -3’s divide out, leaving “d” by itself.

7. The -4’s divide out, leaving “y” by itself.
SOLVING INEQUALITIES
Step 1: Combine Like Terms
3y and -7y are like terms.
Since 3y and -7y have opposite signs, we subtract the coefficients. (3 and -7 are the coefficients)
The answer keeps the sign of the integer with the larger absolute value
Add 1 to both sides because: 1 is involved subtraction and the opposite of subtracting is adding=)
Step 2: Add 1 to Both Sides
=32
-1 +1 =0, leaving “-4y” by itself.
We change inequality sign whenever we MULTIPLY OR DIVIDE by a NEGATIVE number=)
Step 3:Divide by 4 & Make a Clean Sweep
A positive divided by a negative equals a negative. 32 divided by -4 equals -8.
The -4’s divide out, leaving “y” by itself.
Final Answer

8. The 10’s divide out, leaving “a” by itself.
SOLVING INEQUALITIES
Step 1: Combine Like Terms
9 and 1 are both integers so we add them =10
8a and 2a are like terms so we add the coefficients =10
Step 2: Divide both sides by 10
Divide by 10 because: 10 and a are involved in multiplying… The opposite of multiplying is dividing
Step 3: Make a Clean Sweep
10 divided by 10 equals 1.
The 10’s divide out, leaving “a” by itself.
Final Answer

9. SOLVING INEQUALITIES Final Answer Step 1: Subtract 2 from both sides
Perform adding and subtracting first when solving 2-step inequalities=)
Step 1: Subtract 2 from both sides
Since -7 and -2 have the same sign, add their absolute values.
=0, leaving “x/6” by itself.
Since the numbers are both negative, the answer is negative.
Multiply by 6 because: 6 and x are involved in dividing… The opposite of dividing is multiplying
Step 2: Multiply both sides by 6
Step 3: Make a Clean Sweep
A negative times a positive equals a negative.
-9 times 6 = -54
6 divided by 6 is 1.
1x=x
Final Answer

10. -5 + 5 =0, leaving “x/-4” by itself.
SOLVING INEQUALITIES
Perform adding and subtracting first when solving 2-step inequalities=)
Step 1: Add 5 to both sides
5 + 5 = 10
=0, leaving “x/-4” by itself.
Multiply by -4 because: -4 and x are involved in dividing… The opposite of dividing is multiplying
Step 2: Multiply both sides by -4
Step 3: Make a Clean Sweep
We change inequality sign whenever we MULTIPLY OR DIVIDE by a NEGATIVE number=)
A positive times a negative equals a negative.
10 times -4 = -40
4 divided by 4 is 1.
1x=x
Final Answer

11. SOLVING INEQUALITIES Final Answer Step 2: Subtract 5 from both sides.
Step 1: Distribute the negative sign to each term inside the parenthesis.
Another way to write the negative sign is as a -1=)
Step 2: Subtract 5 from both sides.
= 10
=0, leaving “-1b” by itself.
Step 3: Divide both Sides by -1
We change inequality sign whenever we MULTIPLY OR DIVIDE by a NEGATIVE number=)
Step 4: Make a Clean Sweep
A positive divided by a negative equals a negative. 10 divided by -1 equals -10
The -1’s divide out, leaving “b” by itself.
Final Answer