equations and inequalities quick review quick guide to solving equations and inequalities
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Equations and Inequalities Quick Review
Quick guide to solving Equations and Inequalities
Tips:You solve two-step equations/inequalities by undoing one operations at a time.
1. First undo Addition/Subtraction (if the term is being added you subtract , if the term is being subtracted you add)
2. Second undo the Multiplication/Division (if the term is being added you subtract , if the term is being subtracted you add)
5 10 5 10a a 5 5 5 +5
5 15a a
5 10 105
aa
5 105 10 5
5 5 5
a a
2 50a a
Goes to 0
Remember equations have one solution and inequalities have a solution set (multiple
solutions)
Solving One-Step Equations
Adding Subtracting
7 15n 7 15n 7 7 7 7
22n 8nRemember like
terms need to go together and you add if the term is
subtracted
Remember like terms need to go together and you
subtract if the term is added
Solving One-Step Equations
Multiplying Dividing
155
n
75n 3nRemember like
terms need to go together and you
multiply if the term is divided
Remember like terms need to go together and you
divide if the term is multiplied
5
5 5 15n 5 5
Solving Two-Step EquationsRemember undo Addition/Subtraction the undo Multiplication/Division
2 7 15n 7 7
2 22n 2 2
Add 7 to both sides
Divide by 2 on both sides
11n Done!
Solving Multi-Step Equations
Remember combine like terms undo Addition/Subtraction the undo Multiplication/Division
2 7 9 15n n
7 7 11 22n 11 11
Add 7 to both sides
Divide by 11 on both sides
2n Done!
11 7 15n Combine like terms 2n and 9n
Solving Equations w/ Variable on both sides
2 7 15 9n n
7 7 11 22n 11 11
Add 7 to both sides
Divide by 11 on both sides
2n Done!
11 7 15n
Combine like terms 2n and 9n add 9n to both sides9 9n n
INEQUALITIESQuick Review
Read, Write, and Graph
Greater Than
Less Than
Greater Than or equal to
Less Than or equal to
2n
2n 3n
3n
2 3
2 3
Solving One-Step Inequalities
Adding Subtracting
7 15n 7 15n 7 7 7 7
22n 8nRemember like
terms need to go together and you add if the term is
subtracted
Remember like terms need to go together and you
subtract if the term is added
Checking One-Step Inequalities Adding Subtracting
7 15n 7 15n 7 7 7 7
22n 8nCheck: Pick a number in the solution set
Check: Pick a number in the solution set
0 7 15 7 15
0 7 15 7 15
Any number less than or equal to 22 is in the
solution set
Any number less than or equal to 8 is in the solution
set
Solving One-Step Inequalities
Multiplying Dividing
>155
n
75n 3n
DON’T FORGET TO FLIP THE SIGN WHEN YOU
MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER
DON’T FORGET TO FLIP THE SIGN WHEN YOU
MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER
5
5 5 >15n 5 5
Checking One-Step InequalitiesMultiplying Dividing
>155
n
75n 3n 5
5 5 >15n 5 5
Check: Pick a number in the solution set
Check: Pick a number in the solution set
Any number greater than 75 is in the solution set
Any greater than 3 is in the solution set
100 >15
520 15
5 10 >15
50 15
Compound Inequalities
“or” “and”
5 or 5f f 5 5w 5 and 5w w
5f
5f
together
5w
5w
together
5
5
5 5
5
5
5 5
Rewrit
e with
varia
ble
first
Solving Two-Step InequalitiesRemember undo Addition/Subtraction the undo Multiplication/Division
2 7 15n 7 7
2 22n 2 2
Add 7 to both sides
Divide by 2 on both sides
11n Done!
Checking Two-Step InequalitiesRemember undo Addition/Subtraction the undo Multiplication/Division
2 7 15n 7 7
2 22n 2 2
11n
Check: Pick a number in the solution set
Any number less than or equal to 11 is in the solution set
2 0 7 15
7 15
Solving Two-Step InequalitiesRemember undo Addition/Subtraction the undo Multiplication/Division
2 7 15n 7 7
2 22n 2 2
Add 7 to both sides
Divide by -2 on both sides
11nRemember to flip the sign when
multiplying or dividing by a negative number
Checking Two-Step InequalitiesRemember undo Addition/Subtraction the undo Multiplication/Division
Check: Pick a number in the solution set
Any number less than or equal to 11 is in the solution set
2 0 7 15
7 15
2 7 15n 7 7
2 22n 2 2
11n
Solving Multi-Step Inequalities
Remember combine like terms undo Addition/Subtraction the undo Multiplication/Division
2 7 9 15n n
7 7 11 22n 11 11
Add 7 to both sides
Divide by 11 on both sides
2n Done!
11 7 15n Combine like terms 2n and 9n
Checking Multi-Step Inequalities
Check: Pick a number in the solution set
Any number less than or equal to 11 is in the solution set
7 15
2 7 9 15n n
7 7
11 22n 11 11
2n
11 7 15n
11 0 7 15
Solving Inequalities w/ Variable on both sides
2 7 15 9n n
7 7 11 22n 11 11
Add 7 to both sides
Divide by -11 on both sides
2n Done!
11 7 15n
Combine like terms -2n and 9n subtract 9n to both sides9 9n n
Flip the sign
Checking Inequalities w/ Variable on both sides
2 7 15 9n n
7 7
11 22n 11 11
2n
11 7 15n 9 9n n
Check: Pick a number in the solution set
Any number less than or equal to 11 is in the solution set
7 15
11 0 7 15
Example:2 1 5
3 6 2
x x
2 1 5
3 6 2
x x
2 1 3
2 1 3
4 1 15
6 6 6
x x
Get common denominators
4 4
6 6
x x
1 11
6 6
x
1 11
6 6
x 6 6
1
11x
1 11x 11 11
Remember to put the variable
first
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