9/18/2017 – Pop Quiz Question 1) 2x+4≥ 24 Solve for x Graph Question 2 8 < -5b -2 Step 1 Step 2 Question 3) m > 2n + b Solve for b

Translating Inequalities Old Math Symbols > Greater than < Less than New Math Symbols Greater than or equal to Less than or equal to

Identify Key Words Read the mathematical problem and identify key terms or phrases that can be translated into an inequality symbol.

Greater than or equal to Key Vocabulary Phrase Meaning Mathematical Symbol At most No more than Less than or equal to At least No greater than Greater than or equal to

Examples Verbal Expression You can spend at most $20 Meaning You can spend $20 or any amount less than $20 Math Expression A person must be at least 18 to vote A person who is 18 years old or any age older than 18 may vote

Additional Key Phrases Symbol Exceeds Is more than Is at least Is at most

Practice Problems More than 18,000 fans attended the Kings’ opening hockey game at the Staples Center in Los Angeles. Your height is greater than 40 inches. The sum of two numbers is at most 6.

Memory Strategy Vocabulary Word Translation At Most and no More than Less than or equal to At Least and no Less than Greater than or equal to

Literal Equations solve literal equations (formulas) for a specified variable. Standard: SOL: A.4a A literal equation is an equation that contains more than one variable. When solving a literal equation, you rearranging the equation to isolate the variable.

1) Solve 2x - 4y = 7 for x To get x by itself, what is the first step? Add 2x Subtract 2x Add 4y Subtract 4y Answer Now

1) Solve 2x - 4y = 7 for x Use a DO-UNDO chart to help determine the steps Ask yourself, What is the first thing we are doing to x? What is the second thing? DO UNDO · 2 -4y Follow the steps in the ‘undo’ column to isolate the variable. +4y ÷ 2 Complete the undo column by writing the opposite operations in opposite order.

1) Solve 2x - 4y = 7 for x + 4y + 4y 2x = 7 + 4y 2 2 Draw “the river” D U · 2 -4y +4y ÷ 2 + 4y + 4y 2x = 7 + 4y 2 2 Draw “the river” Add 4y to both sides Simplify Divide both sides by 2 Does it simplify? This fraction cannot be simplified because both terms in the numerator are not divisible by 2.

2) Solve 2x - 4y = 7 for y To get y by itself, what is the first step? Add 2x Subtract 2x Add 4y Subtract 4y Answer Now

2) Solve 2x - 4y = 7 for y - 2x - 2x -4y = 7 - 2x -4 -4 D U · -4 +2x -2x ÷ -4 - 2x - 2x -4y = 7 - 2x -4 -4 Draw “the river” Subtract 2x from both sides Simplify Divide both sides by -4 Does it simplify? Nope!

3) Solve for y. What is the first step? Multiply by 3 Divide by 3 Add a Subtract a Answer Now

3) Solve for y: y + a = 3c -a -a y = 3c - a Draw “the river” D U + a ÷ 3 · 3 - a Draw “the river” Clear the fraction – multiply both sides by 3 Simplify Subtract a from both sides y + a = 3c -a -a y = 3c - a

4) Solve for y: 4x – 2y = 12 -4x + 12 4x - 12 -2x + 6 2x - 6 Answer Now

4) Solve for y: 4x – 2y = 12 - 4x - 4x -2y = 12 – 4x -2 -2 y = -6 + 2x D U 4) Solve for y: 4x – 2y = 12 · -2 + 4x - 4x ÷ -2 - 4x - 4x -2y = 12 – 4x -2 -2 y = -6 + 2x or y = 2x - 6 Draw “the river” Subtract 4x from both sides Simplify Divide both sides by -2 Does it simplify? Yes!

5) The formula for the volume of a rectangular prism is V = LWH 5) The formula for the volume of a rectangular prism is V = LWH. Which equation solves the formula for L? L = V - WH Answer Now

6) The formula for the volume of a pyramid is V = 6) The formula for the volume of a pyramid is V = . Which equation solves the formula for h? h = 3Vb Answer Now