Prerequisite Skills Pg. 130 #1-13 Copy and complete the statement. ANSWER 8 5 3x, 7x 1. In the expression 3x x, and are like terms. ?? 2. The reciprocal of is. 5 8 ?
Prerequisite Skills SKILLS CHECK Simplify the expression. 3. 5x – (6 – x) 4. 3(x – 9) – (x + 2) 6. x(7 + x) + 9x 2 ANSWER 6x – 6 ANSWER 3x – 43 ANSWER 4x + 31 ANSWER 10x 2 + 7x Write the percent as a decimal % ANSWER % ANSWER % ANSWER % ANSWER 1.5
Prerequisite Skills Find the perimeter of the rectangle. ANSWER 46 ft ANSWER 68 cm ANSWER 30 in SKILLS CHECK
Animated Activity Classzone.com Modeling One-Step Equations
Vocabulary Golden Rule of Algebra: Do unto one side what you do to the other!!! Inverse Operations: –Examples: Properties to solve equations: 1.) Addition Property of Equality: 2.) Subtraction Property of Equality: 3.) Multiplication Property of Equality: 4.) Division Property of Equality: adding the same # to each side produces an equivalent equation subtracting the same # to each side produces an equivalent equation multiplying the same # to each side produces an equivalent equation dividing the same # to each side produces an equivalent equation 2 operations that UNDO each other add & subtract; multiply & divide
Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. – 7 – 7 Use subtraction property of equality: Subtract 7 from each side. x = –3x = –3 Simplify. ANSWERThe solution is –3. CHECK Substitute –3 for x in the original equation. x + 7 = 4x + 7 = 4 Write original equation. –3 + 7 = 4 ? Substitute – 3 for x. 4 = 44 = 4 Simplify. Solution checks.
Solve an equation using addition EXAMPLE 2 & 3 Solve x – 12 = 3. Add 12 to each side Simplify. x = 15 Solve –6x = 48. x = –8 –6x –6 48 –6 = Divide each side by –6. Simplify.
GUIDED PRACTICE for Examples 1, 2, and 3 1. y + 7 = 10 ANSWER 3 Solve the equation. Check your solution. 2. x – 5 = 3 8 ANSWER 3. q – 11 = –5 6 ANSWER 4. 6 = t – 28 ANSWER 5. 4x = ANSWER 6. –65 = –5y 13 ANSWER 7. 6w = –54 –9–9 ANSWER = –8n –3–3 ANSWER
Solve an equation using multiplication EXAMPLE 4 4 x 4 = 4 5 Multiply each side by 4. x = 20 Simplify. = 5. x 4 Solve SOLUTION
GUIDED PRACTICE for Example = 9 t –3 Solve the equation. Check your Solution. –27 ANSWER c 7 = 42 ANSWER z –2 = –26 ANSWER 12. = –11 a 5 –55 ANSWER
Solve an equation by multiplying by a reciprocal EXAMPLE 5 SOLUTION x = – Solve 7 2 – The coefficient of x is. 7 2 – The reciprocal of. 2 7 – is ( ) ( x ) = 2 7 – 7 2 – 7 2 – 4 2 Multiply each side by the 7 – reciprocal,. x = –14 Simplify. ANSWER The solution is –14. Check by substituting –14 for x in the original equation. CHECK Substitute –14 for x. 4 = 4 Simplify. Solution checks. (–14) = 4 ? 2 7 –
GUIDED PRACTICE for Example 5 Solve the equation. Check your Solution. w = ANSWER 12 p = ANSWER =9 = –3 4 m ANSWER – –8 = –4 5 v ANSWER 10
EXAMPLE 6 Write and solve an equation Let r represent Crawford's speed in meters per second. Write a verbal model. Then write and solve an equation. SOLUTION OLYMPICS In the 2004 Olympics, Shawn Crawford won the 200 meter dash. His winning time was seconds. Find his average speed to the nearest tenth of a meter per second r = 200 = r r Crawford's average speed was about 10.1 meters per second. ANSWER
GUIDED PRACTICE for Example WHAT IF? In example 6, suppose Shawn Crawford ran 100 meters at the same average speed he ran the 200 meters. How long would it take him to run 100 meters ? Round your answer to nearest tenth of a second. 9.9 sec ANSWER
Animated Activity Classzone.com Box Jellyfish
Check Yourself Pg #4-28eoe, 30-48e, 55, 61, 64-66