Prerequisite Skills Pg. 130 #1-13 Copy and complete the statement. ANSWER 8 5 ANSWER 3x, 7x 1. In the expression 3x + 7 + 7x, and are like terms. ? ? 2. The reciprocal of is . 5 8 ?
Jan 01, 2016
Prerequisite Skills Pg. 130 #1-13
Copy and complete the statement.
ANSWER 85
ANSWER 3x, 7x
1. In the expression 3x + 7 + 7x, and are like terms.
? ?
2. The reciprocal of is .58
?
Prerequisite Skills SKILLS CHECK
Simplify the expression.
3. 5x – (6 – x)
4. 3(x – 9) – 16
5. 23 + 4(x + 2)
6. x(7 + x) + 9x2
ANSWER 6x – 6
ANSWER 3x – 43
ANSWER 4x + 31
ANSWER 10x2 + 7x
Write the percent as a decimal.
7. 54% ANSWER 0.54
8. 99% ANSWER 0.99
9. 12.5% ANSWER 0.125
10. 150% ANSWER 1.5
Prerequisite Skills
Find the perimeter of the rectangle.
ANSWER 46 ft
ANSWER 68 cm
ANSWER 30 in.
11.
12.
13.
SKILLS CHECK
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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 subtractionEXAMPLE 1
Solve x + 7 = 4.
– 7 – 7Use subtraction property of equality: Subtract 7 from each side.
x = –3 Simplify.
ANSWER The solution is –3.
CHECK Substitute –3 for x in the original equation.
x + 7 = 4 Write original equation.
–3 + 7 = 4?
Substitute –3 for x.
4 = 4 Simplify. Solution checks.
Solve an equation using addition
EXAMPLE 2 & 3
Solve x – 12 = 3.Add 12 to each side.+ 12 + 12Simplify.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 8ANSWER
3. q – 11 = –5 6ANSWER
4. 6 = t – 2 8ANSWER
5. 4x = 48 12ANSWER
6. –65 = –5y 13ANSWER
7. 6w = –54 –9ANSWER
8. 24 = –8n –3ANSWER
Solve an equation using multiplicationEXAMPLE 4
4 x4 = 4 5 Multiply each side by 4.
x = 20 Simplify.
= 5.x 4Solve
SOLUTION
GUIDED PRACTICE for Example 4
9. = 9t–3
Solve the equation. Check your Solution.
–27ANSWER
10. 6 c7= 42ANSWER
11. 13 z–2= –26ANSWER
12. = –11a 5 –55ANSWER
Solve an equation by multiplying by a reciprocal
EXAMPLE 5
SOLUTION
x = 4.27
–Solve
72–The coefficient of x is .
72
–The reciprocal of .27
–is
( )(x ) =27
–72
–72
– 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 ?
27
–
GUIDED PRACTICE for Example 5
Solve the equation. Check your Solution.
w = 105613. ANSWER 12
p = 142314. ANSWER 21
15. 9 = –3
4m ANSWER –12
16. –8 = –4
5v 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 19.79 seconds. Find his average speed to the nearest tenth of a meter per second.
19.7920019.79 19.79 r=
200 = r 19.79
10.1 r
Crawford's average speed was about 10.1 meters persecond.
ANSWER
GUIDED PRACTICE for Example 6
17. 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 torun 100 meters? Round your answer to nearest tenth of a second.
9.9 secANSWER
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Box Jellyfish
Check Yourself
Pg. 137-140 #4-28eoe, 30-48e, 55, 61, 64-66