Review

When substituting a value into an expression, use parentheses. To evaluate a variable expression, you write the expression, substitute a number for each variable, and simplify. Evaluate the variable expression when b = 3. The problem.7b7b Substitute.7(3) Simplify. 21 In algebra work downward in columns. Skip one line after the answer. Highlight or circle your answer. You may find it helpful to fold your paper in half lengthwise to create 2 columns.

Example 3 Evaluate the variable expression when b = 3. 6 Get into the habit of using parentheses when you substitute. It will help eliminate errors when the problems are more complex!

Example 4 Evaluate the variable expression when b = 3. 9

A formula is an algebraic equation that relates two or more quantities. distance = rate time Distance Perimeter A measure of the distance around a geometric figure. triangle rectangle Area rectangle triangle square units of the interior region of a two dimensional figure or the surface of a three dimensional figure.

Example 5 Use a variable expression to find the distance traveled by a truck moving at an average speed of 65 miles per hour for 6 hours. 1.Write the formula. d = rt 2. Substitute. = (65)(6) 3. Simplify. = Write a sentence. The truck traveled 390 miles. Note: Include the label in your sentence. Use one equal sign per line of work. Keep the equal signs in a line!

Evaluate when x = 6. The problem. Substitute. Write factors. x2x2 (6)2 (6)(6) Simplify.36 A power applies only to what is directly in front of it. You could write in factored form and then substitute. x2x2 (6)(6) 36

Example 4 Evaluate when m = 4 and n = Write problem. 2. Substitute. (m + n)2 ((4) + (3))2 3. Simplify within parentheses. (7)2 4. Evaluate power. 49 When you evaluate exponential expressions, work within grouping symbols first. ( ), [ ],{ } Remember: In algebra work downward. Highlight or circle your answer. Skip one line after the answer.

Example 5 Evaluate when m = 4 and n = Write problem. 2. Substitute. 3. Write factors. (m2) + (n2) ((4)2) + ((3)2) (4 4) + (3 3) Optional Step 4. Simplify within parentheses When you evaluate exponential expressions, work within grouping symbols first. ( ), [ ],{ } 5. Simplify. 25 When parentheses are nested work from the inside going out.

Example 6 Evaluate when a = Write problem. 2. Substitute. 2a2 2(5)2 3. Evaluate power.2(25) 4. Simplify. 50 Remember a power applies only to what is directly in front of it!

Example 7 Evaluate when a = Write problem. 2. Substitute. (2a)2 (2(5))2 3. Simplify within parentheses. (10)2 4. Evaluate power. 100

Example 8 A box has the shape of a cube. Each edge s is 8 inches long. Find the volume in cubic inches. 1. Write formula. 2. Substitute. V = s3 = (8)3 3. Write factors. Optional Step = Simplify. = Write a sentence.The volume of the box is 512 cubic inches. This cannot be written as 5123 inches!

Order of Operations The order of operations are: –P arenthesis –E xponents –M ultiplication & D ivision, in order, from left to right –A ddition & S ubtraction, in order, from left to right PEMDAS is used to remember the order of operations.

Example #1 Evaluate the expression 3x when x = 4 3x (4 2 ) + 1 3(16) Write the expression 2. Substitute 4 for x 3. Evaluate the power Answer: The value of the expression is Evaluate the product 5. Evaluate the sum 49

Example #2 Evaluate the expression 32  x 2 – 1 when x = 4 32  x 2 – 1 32  (4 2 ) – 1 32  16 – 1 1. Write the expression 2. Substitute 4 for x 3. Evaluate the power Answer: The value of the expression is 1 2 – 1 4. Evaluate the quotient 5. Evaluate the difference 1

Example #3 – Using a fraction bar 1. Write the expression 2. Evaluate the power 3. Simplify the numerator 4. Simplify the denominator working from left to right 5. Simplify the fraction

Your Turn Evaluate the expression for the given value of the variable

Your Turn Evaluate the expression

Your Turn Solutions

Example #1 Check whether the numbers 2, 3 & 4 are solutions to the equation 4x – 2 = 10 4x – 2 = 10 4(2) – 2 = 10 8 – 2 = Write the equation 2. Substitute 2 for x 3. Simplify Conclusion: 2 is not a solution to the equation 6 = Analyze the result 5. Draw the conclusion 6 ≠ 10 This symbol means does not equal

Example #2 Check whether the numbers 2, 3 & 4 are solutions to the equation 4x – 2 = 10 4x – 2 = 10 4(3) – 2 = – 2 = Write the equation 2. Substitute 3 for x 3. Simplify Conclusion: 3 is a solution to the equation 10 = Analyze the result 5. Draw the conclusion 10 = 10

Example #3 Check whether the numbers 2, 3 & 4 are solutions to the equation 4x – 2 = 10 4x – 2 = 10 4(4) – 2 = – 2 = Write the equation 2. Substitute 4 for x 3. Simplify Conclusion: 4 is not a solution to the equation 14 = Analyze the result 5. Draw the conclusion 14 ≠ 10

Example #4 Decide if 4 is a solution to the inequality 2x – 1 < 8 2x – 1 < 8 2(4) – 1 < 8 8 – 1 < 8 1. Write the inequality 2. Substitute 4 for x 3. Simplify Conclusion: 4 is a solution to the inequality 7 < 8 4. Analyze the result 5. Draw the conclusion True

Example #5 Decide if 4 is a solution to the inequality x + 4 > 9 x + 4 > > 9 8 > 9 1. Write the inequality 2. Substitute 4 for x 3. Simplify Conclusion: 4 is not a solution to the inequality 8 > 9 4. Analyze the result 5. Draw the conclusion False

Example #6 Decide if 4 is a solution to the inequality x – 3 ≥ 1 x – 3 ≥ 1 4 – 3 ≥ 1 1 ≥ 1 1. Write the inequality 2. Substitute 4 for x 3. Simplify Conclusion: 4 is a solution to the inequality 1 ≥ 1 4. Analyze the result 5. Draw the conclusion True

Your Turn – Checking Equations Check whether the given number is a solution to the equation 1.3b + 1 = 13b=4 2.6d – 5 = 20d = 5 3.2y = 5y = 1 4.p 2 – 5 = 20 p = 6 5.m + 4m = 60 – 2mm = 10

Your Turn – Checking Inequalities Check whether the given number is a solution to the inequality 6.n – 2 < 6n = 3 7.4p – 1 ≥ 8p = 2 8.y 3 – 2 ≤ 8y = – d ≥ 4d = 5 d 10. a(3a +2) > 50a = 4

Your Turn Solutions 1.True 2.False 3.True 4.False 5.False 6.True 7.False 8.True 9.True 10.True