1. Warm-Up #2 Simplify the expression. 2. –6(m – 9) + 14m – 20
1. 8b – 3(4 – b)
ANSWER
11b – 12
ANSWER
8m + 34
3. You bought a pair of jeans for n dollars in a city where the sales tax rate is 5%. Write an expression for the total cost of the jeans, including sales tax.
ANSWER
n n, or 1.05n

4. Solve an equation with a variable on one side
EXAMPLE 1
Solve an equation with a variable on one side
Solve 4 5
x + 8 = 20. 4 5
x + 8 = 20
Write original equation. 4 5
x = 12
Subtract 8 from each side.
x = (12) 5 4
Multiply each side by , the reciprocal of 5 4
x = 15
Simplify.
ANSWER
The solution is 15.
CHECK
x = 15 in the original equation. 4 5
x + 8 =
(15) + 8 = = 20

5. EXAMPLE 2
Write and use a linear equation
During one shift, a waiter earns wages of $30 and gets an additional 15% in tips on customers’ food bills. The waiter earns $105. What is the total of the customers’ food bills?
Restaurant
SOLUTION
Write a verbal model. Then write an equation. Write 15% as a decimal.

6. Write and use a linear equation
EXAMPLE 2
Write and use a linear equation
105 = x
Write equation.
75 = 0.15x
Subtract 30 from each side.
500 = x
Divide each side by 0.15.
The total of the customers’ food bills is $500.
ANSWER

7. GUIDED PRACTICE
for Examples 1 and 2
Solve the equation. Check your solution.
x + 9 = 21
ANSWER
The solution is x = 3.
x – 41 = – 13
ANSWER
The solution is x = 4. 3. 3 5 –
x + 1 = 4
ANSWER
The solution is -5.

8. Solve an equation using the distributive property
EXAMPLE 4
Solve an equation using the distributive property
Solve 3(5x – 8) = –2(–x + 7) – 12x.
3(5x – 8) = –2(–x + 7) – 12x
Write original equation.
15x – 24 = 2x – 14 – 12x
Distributive property
15x – 24 = – 10x – 14
Combine like terms.
25x – 24 = –14
Add 10x to each side.
25x = 10
Add 24 to each side.
x = 2 5
Divide each side by 25 and simplify.
ANSWER
The solution 2 5

9. Solve an equation using the distributive property
EXAMPLE 4
Solve an equation using the distributive property
CHECK 2 5
3( – 8) –2(– ) – 12 = ? 2 5
Substitute for x.
3(–6) –14 – 4 5 = ? 24
Simplify.
– 18 = – 18
Solution checks.

10. GUIDED PRACTICE
for Examples 3, 4, and 5
Solve the equation. Check your solution.
5. –2x + 9 = 2x – 7
ANSWER
The correct answer is 4.
– x = –6x + 15
ANSWER
The correct answer is 1.
(x + 2) = 5(x + 4)
ANSWER
The solution is –7.

11. GUIDED PRACTICE
for Examples 3, 4, and 5
Solve the equation. Check your solution.
8. –4(2x + 5) = 2(–x – 9) – 4x
ANSWER
The solution x = – 1
x x = 39 1 4 2 5 9.
ANSWER
The correct answer is 60

13. Rewrite a formula with two variables
EXAMPLE 1
Rewrite a formula with two variables
Solve the formula C = 2πr for r. Then find the radius of a circle with a circumference of 44 inches.
SOLUTION
STEP 1
Solve the formula for r.
C = 2πr
Write circumference formula. C 2π
= r
Divide each side by 2π.
STEP 2
Substitute the given value into the rewritten formula.
r = C 2π = 44 7
Substitute 44 for C and simplify.
The radius of the circle is about 7 inches.
ANSWER

14. GUIDED PRACTICE
for Example 1
The formula for the distance d between opposite vertices of a regular hexagon is d = where a is the distance between opposite sides. Solve the formula for a. Then find a when d = 10 centimeters. 2. 2a 3
SOLUTION d 3
a = 2 3 5
When d = 10cm, a = or cm

15. Rewrite a formula with three variables
EXAMPLE 2
Rewrite a formula with three variables
Solve the formula P = 2l + 2w for w. Then find the width of a rectangle with a length of 12 meters and a perimeter of 41 meters.
SOLUTION
Solve the formula for w.
STEP 1
P = 2l + 2w
Write perimeter formula.
P – 2l = 2w
Subtract 2l from each side.
P – 2l 2
= w
Divide each side by 2.

16. Rewrite a formula with three variables
EXAMPLE 2
Rewrite a formula with three variables
Substitute the given values into the rewritten formula.
STEP 2
41 – 2(12) 2
w =
Substitute 41 for P and 12 for l.
w = 8.5
Simplify.
The width of the rectangle is 8.5 meters.
ANSWER

17. GUIDED PRACTICE
for Example 2
Solve the formula P = 2l + 2w for l. Then find the length of a rectangle with a width of 7 inches and a perimeter of 30 inches. 3.
Length of rectangle is 8 in.
ANSWER
Solve the formula A = lw for w. Then find the width of a rectangle with a length of 16 meters and an area of 40 square meters. 4.
Write of rectangle is 2.5 m
w = A l
ANSWER

18. GUIDED PRACTICE
for Example 2
Solve the formula for the variable in red. Then use the given information to find the value of the variable.
A = 1 2 bh 5.
Find h if b = 12 m
and A = 84 m2.
ANSWER = h 2A b

19. GUIDED PRACTICE
for Example 2
Solve the formula for the variable in red. Then use the given information to find the value of the variable.
A = 1 2 bh 6.
and A = 9 cm2.
Find b if h = 3 cm
ANSWER = b 2A h

20. GUIDED PRACTICE
for Example 2
Solve the formula for the variable in red. Then use the given information to find the value of the variable.
A = 1 2 7.
(b1 + b2)h
Find h if b1 = 6 in.,
b2 = 8 in., and A = 70 in.2
ANSWER
h = 2A
(b1 + b2)

21. Rewrite a linear equation
EXAMPLE 3
Rewrite a linear equation
Solve 9x – 4y = 7 for y.
SOLUTION
Solve the equation for y.
STEP 1
9x – 4y = 7
Write original equation.
–4y = 7 – 9x
Subtract 9x from each side.
y = 9 4 7 – + x
Divide each side by –4.

22. Rewrite a nonlinear equation
EXAMPLE 4
Rewrite a nonlinear equation
Solve 2y + xy = 6 for y.
SOLUTION
Solve the equation for y.
STEP 1
2y + x y = 6
Write original equation.
(2+ x) y = 6
Distributive property
y = 6
2 + x
Divide each side by (2 + x).

23. GUIDED PRACTICE
for Examples 3 and 4
Solve the equation for y. Then find the value of y when x = 2.
8. y – 6x = 7
9. 5y – x = 13
10. 3x + 2y = 12
y = x
y = 19
ANSWER
y = x 5 13 +
y = 3
ANSWER
y = – 3x 2
+ 6
ANSWER
y = 3

24. GUIDED PRACTICE
for Examples 3 and 4
Solve the equation for y. Then find the value of y when x = 2.
11. 2x + 5y = –1
12. 3 = 2xy – x
13. 4y – xy = 28 2x 5 –1 –
y = –1
y =
ANSWER
y = 1 4
3 +x 2x
ANSWER
y = 14 28
4 – x
y =
ANSWER

25. CLASSWORK
Workbook 1-3 (1-25 odd)
Workbook 1-4 (1-25 odd)