Simplifying Expressions 2 * x = 2x A number times a variable, Smush together 5*y = x * x = x2 A variable times a variable, Use an exponent z * z = 3x * 5 = 15x Multiply the numbers, keep the variable 4y * 2 = 3x * x = 3x2 Multiply the variables, keep the number 7y * y =

Warm-Up Ronisha and Kalyn are arguing whether the answer to 8(27) can be found by doing the following work. Do you think this is correct? Explain. Yes, this method can be used because 27 is still being multiplied by 8. 27 is just split into 20 and 7 first before it is multiplied by 8.

One-Step Equations and Inequalities What is an equation? My Definition Two mathematical expressions that are set equal to one another. Characteristics Has an equal sign Whatever you do to one side of the equal sign, you must do to the other side of the equal sign. Examples 4 + x = 17 X – 5 = y Non-examples Y – 7 13 8x + 2y + 8 Equation

Inverse Operations Inverse operations are operations that undo each other (opposites) INVERSE OPERATIONS Addition + Subtraction - Multiplication x Division - Square Square Root Recognizing Subtraction Recognizing Multiplication Recognizing Division Recognizing Addition Term with a negative sign in front X – 5 -3 + x Number & variable are side-by-side 5x xy Number /variable are separated by fraction bar 8 4 𝑥 7 Positive number by itself X + 3 3 + x

Do/Undo Method Solve for x + 7 = 22 DO UNDO Solve for x X = 15 Add 7 Subtract 7 x + 7 = 22 - 7 -7 x + 0 = 15

Think of this equation as a balance scale. 1) Solve r - 16 = 7 Think of this equation as a balance scale. r - 16 7 = Whatever you do to one side has to be done to the other to keep it balanced!

1) Solve r - 16 = 7 To solve, you must get the variable by itself. What number is on the same side as r? 16 To get r by itself, we must undo the “add 16”. What is the opposite of subraction? Add 16

1) Solve r - 16 = 7 r - 16 = 7 + 16 +16 r = 23 23 - 16 = 7 Draw “the river” to separate the equation into 2 sides Subtract 16 from both sides Simplify vertically Check your answer by substituting your answer back into the problem

2) Solve x + 2 = 3 Get the variable by itself. What is your first step? Add 2 to both sides Subtract 2 from both sides Add 3 to both sides Subtract 3 from both sides Answer Now

2) Solve x + 2 = 3 - 2 - 2 x = 1 1 + 2 = 3 Draw “the river” to separate the equation into 2 sides Subtract 2 from both sides Simplify vertically Check your answer by substituting your answer back into the problem On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!

3) Solve 8 = m - 3 m = 5 m = 11 m = 24 m = 8/3 Answer Now

3) Solve 8 = m - 3 + 3 + 3 11= m 8 = 11 - 3 Draw “the river” to separate the equation into 2 sides Add 3 to both sides Simplify vertically Check your answer by substituting your answer back into the problem

Solution set of an inequality Inequalities Vocabulary Write the term that best completes each statement. A(n)________________ in one variable is the set of all points on a number line that makes the inequality true. A(n) ___________________begins at a starting point and goes on forever in one direction. Any mathematical sentence that has an inequality symbol is a(n)____________________________ . The ____________________________is the set of all numbers that make the inequality true. Word Bank Inequality Ray Graph of an inequality Solution set of an inequality

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Examples of Graphs of Inequalities X is equal to three A number is at least 3 a number is not more than 3 A number is greater than 3 a number is less than 3