Simplify the expression.
1. 8b – 3(4 – b)
ANSWER
2. –6(m – 9) + 14m – 20
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 + 0.05n, or 1.05n
EXAMPLE 1
Solve an equation with a variable on one side
Solve 4 x + 8 = 20.
5
4 x + 8 = 20
5
4 x = 12
5
x = 5 (12)
4
x = 15
Write original equation.
Subtract 8 from each side.
Multiply each side by 5 ,
the reciprocal of 4 . 4
5
Simplify.
ANSWER The solution is 15.
CHECK x = 15 in the original equation.
4 x + 8 = 4 (15) + 8 = 12 + 8 = 20
5
5
EXAMPLE 2
Write and use a linear equation
Restaurant
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?
SOLUTION
Write a verbal model. Then write an equation. Write
15% as a decimal.
EXAMPLE 2
Write and use a linear equation
105 = 30 + 0.15x
75 = 0.15x
500 = x
Write equation.
Subtract 30 from each side.
Divide each side by 0.15.
ANSWER
The total of the customers’ food bills is $500.
GUIDED PRACTICE
for Examples 1 and 2
Solve the equation. Check your solution.
1.
4x + 9 = 21
ANSWER The solution is x = 3.
2.
7x – 41 = – 13
ANSWER The solution is x = 4.
3. – 3 x + 1 = 4
5
ANSWER The solution is -5.
EXAMPLE 4
Solve an equation using the distributive property
Solve 3(5x – 8) = –2(–x + 7) – 12x.
3(5x – 8) = –2(–x + 7) – 12x
15x – 24 = 2x – 14 – 12x
15x – 24 = – 10x – 14
25x – 24 = –14
25x = 10
x= 2
5
ANSWER The solution 2
5
Write original equation.
Distributive property
Combine like terms.
Add 10x to each side.
Add 24 to each side.
Divide each side by 25 and simplify.
EXAMPLE 4
Solve an equation using the distributive property
CHECK
3(5 2 – 8) =? –2(– 2 + 7) – 12
5
5
3(–6) =? 4 –14 – 24
5
5
– 18 = – 18
2
5
Substitute 2 for x.
5
Simplify.
Solution checks.
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.
6.
10 – x = –6x + 15
ANSWER The correct answer is 1.
7.
3(x + 2) = 5(x + 4)
ANSWER The solution is –7.
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
9.
1 x + 2 x = 39
4
5
ANSWER The correct answer is 60
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
Divide each side by 2π.
2π = r
STEP 2 Substitute the given value into the rewritten formula.
C 44
7 Substitute 44 for C and simplify.
r = 2π = 2π
ANSWER The radius of the circle is about 7 inches.
GUIDED PRACTICE
2.
for Example 1
The formula for the distance d between opposite
vertices of a regular hexagon is d = 2a where a is
3
the distance between opposite sides. Solve the
formula for a. Then find a when d = 10 centimeters.
SOLUTION
d 3
a= 2
When d = 10cm, a = 5 3
or
8.7cm
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
STEP 1 Solve the formula for w.
P = 2l + 2w
Write perimeter formula.
P – 2l = 2w
Subtract 2l from each side.
P – 2l = w
2
Divide each side by 2.
EXAMPLE 2
Rewrite a formula with three variables
STEP 2
Substitute the given values into the rewritten formula.
41 – 2(12)
w=
2
Substitute 41 for P and 12 for l.
w = 8.5
Simplify.
ANSWER
The width of the rectangle is 8.5 meters.
GUIDED PRACTICE
for Example 2
3. 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.
ANSWER
Length of rectangle is 8 in.
4. 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.
ANSWER
w= A
l
Write of rectangle is 2.5 m
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.
1 bh
A
=
5.
2
Find h if b = 12 m
and A = 84 m2.
ANSWER
2A = h
b
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.
1 bh
A
=
6.
Find b if h = 3 cm
2
and A = 9 cm2.
ANSWER
2A = b
h
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.
1 (b + b )h
A
=
7.
2
Find h if b1 = 6 in.,
2 1
b2 = 8 in., and A = 70 in.2
ANSWER
h=
2A
(b1 + b2)
EXAMPLE 3
Rewrite a linear equation
Solve 9x – 4y = 7 for y.
SOLUTION
STEP 1 Solve the equation for y.
9x – 4y = 7
Write original equation.
Subtract 9x from each side.
–4y = 7 – 9x
y = – 7 + 9 x Divide each side by –4.
4
4
EXAMPLE 4
Rewrite a nonlinear equation
Solve 2y + xy = 6 for y.
SOLUTION
STEP 1 Solve the equation for y.
2y + x y = 6
Write original equation.
(2+ x) y = 6
Distributive property
y=
6
2+x
Divide each side by (2 + x).
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
ANSWER
ANSWER
ANSWER
y = 7 + 6x
y = 19
13
x
y= 5 + 5
y=3
y = – 3x + 6
2
y=3
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
ANSWER
ANSWER
y = –1 – 2x
5
5
y = –1
+x
y = 32x
1
y= 1
4
13. 4y – xy = 28
ANSWER
y = 428
–x
y = 14
CLASSWORK
Workbook 1-3 (1-25 odd)
Workbook 1-4 (1-25 odd)