# Equations and Inequalities Quick Review

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Equations and Inequalities Quick Review
Quick guide to solving Equations and Inequalities

Tips: Remember equations have one solution and inequalities have a solution set (multiple solutions) You solve two-step equations/inequalities by undoing one operations at a time. First undo Addition/Subtraction (if the term is being added you subtract , if the term is being subtracted you add) Second undo the Multiplication/Division (if the term is being added you subtract , if the term is being subtracted you add) Goes to 0

Solving One-Step Equations
Adding Subtracting Remember 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 Remember 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

Solving Two-Step Equations
Remember undo Addition/Subtraction the undo Multiplication/Division Add 7 to both sides Divide by 2 on both sides Done!

Solving Multi-Step Equations
Remember combine like terms undo Addition/Subtraction the undo Multiplication/Division Combine like terms 2n and 9n Add 7 to both sides Divide by 11 on both sides Done!

Solving Equations w/ Variable on both sides
Combine like terms 2n and 9n add 9n to both sides Add 7 to both sides Divide by 11 on both sides Done!

Inequalities Quick Review

Read, Write, and Graph Less Than Less Than or equal to Greater Than
Greater Than or equal to

Solving One-Step Inequalities
Adding Subtracting Remember 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 Check: Pick a number in the solution set Check: Pick a number in the solution set 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 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

Checking One-Step Inequalities
Multiplying Dividing 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

Compound Inequalities
Rewrite with variable first “or” “and”

Solving Two-Step Inequalities
Remember undo Addition/Subtraction the undo Multiplication/Division Add 7 to both sides Divide by 2 on both sides Done!

Checking Two-Step Inequalities
Remember 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

Solving Two-Step Inequalities
Remember undo Addition/Subtraction the undo Multiplication/Division Add 7 to both sides Divide by -2 on both sides Remember to flip the sign when multiplying or dividing by a negative number

Checking Two-Step Inequalities
Remember 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

Solving Multi-Step Inequalities
Remember combine like terms undo Addition/Subtraction the undo Multiplication/Division Combine like terms 2n and 9n Add 7 to both sides Divide by 11 on both sides Done!

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

Solving Inequalities w/ Variable on both sides
Combine like terms -2n and 9n subtract 9n to both sides Add 7 to both sides Divide by -11 on both sides Flip the sign Done!

Checking Inequalities w/ Variable on both sides
Check: Pick a number in the solution set Any number less than or equal to 11 is in the solution set

Get common denominators
Example: Remember to put the variable first