Literal EquationsLiteral Equations

ANSWER 2a + 3 = 24

1. Write an equation for “3 more than twice a is 24.”

ANSWER 64 ft2

2. A square has a side length of 8 feet. Find the area ofthe square using the formula A = s2.

Review verbal equations

Literal Equations page 169Literal Equations page 169

1) Solve 2x - 4y = 7 for xTo get x by itself, what is the first step?

1. Add 2x

2. Subtract 2x

3. Add 4y

4. Subtract 4y

1) Solve 2x - 4y = 7 for x

1. Draw the center line

(whatever we do on one side, we must do on the other)

2. Add 4y to both sides

3. Simplify

4. Divide both sides by 2

+ 4y = + 4y

2x = 7 + 4y

2 2

2) Solve 2x - 4y = 7 for yTo get y by itself, what is the first step?

1. Add 2x

2. Subtract 2x

3. Add 4y

4. Subtract 4y

2) Solve 2x - 4y = 7 for y

1. Draw the center line

2. Subtract 2x from both sides

3. Simplify

4. Divide both sides by -4

- 2x = - 2x

-4y = 7 - 2x

-4 -4

3) Solve for y: 4x – 2y = 12

1. y = -4x + 12

2. y = 4x - 12

3. y = -2x + 6

4. y = 2x - 6

1. L = V - WH

2.

3.

4.

3) The formula for the volume of a rectangular prism is V = LWH. Which equation solves the

formula for L?

LV H

W

LV W

H

LV

HW

1. h = 3Vb

2.

3.

4.

4) The formula for the volume of a pyramid is V = . Which equation solves the

formula for h?

1

3bh

h 3b

V

h 3V

b

h V

3b

Subtract b from each side.

Write original equation.

Solve ax + b = c for x.STEP 1

SOLUTION

Solve ax + b = c for x. Then use the solution to solve 2x + 5 = 11. a = 2, b = 5, c = 11

Solve a literal equationEXAMPLE

xc – b

a=

ax + b = c

ax = c – b

Assume a 0. Divide each side by a.

The solution of 2x + 5 = 11 is 3.ANSWER

Simplify.

Substitute 2 for a, 5 for b, and 11 for c.

Solution of literal equation.

Use the solution to solve 2x + 5 = 11.STEP 2

Solve a literal equation

EXAMPLE

11 – 52=

x = c – b

a

= 3

PRACTICE

1. a – bx = c; 12 – 5x = –3

Solve the literal equation for x. Then use the solution to solve the specific equation

; 3ANSWER x = a – c

b

2. ax = bx + c; 11x = 6x + 20

; 4ANSWERc

x =a – b

Divide each side by 2.

Write original equation.

Write 3x + 2y = 8 so that y is a function of x. Solve for y.

EXAMPLE Rewrite an equation

Subtract 3x from each side.

3x + 2y = 8

2y = 8 – 3x

32

y = 4 – x

Multiply each side by 2.

Write original formula.

SOLUTION

Use the rewritten formula to find the height of the triangle shown, which has an area of 64.4 square meters.

b.

Solve the formula for the height h.a.

EXAMPLE 3 Solve and use a geometric formula

The area A of a triangle is given by the formula A = bh where b is the base and h is the height.

12

a. bh12A =

2A bh=

Substitute 64.4 for A and 14 for b.

Write rewritten formula.

Substitute 64.4 for A and 14 for b in the rewritten formula.

b.

Divide each side by b.

EXAMPLE 3 Solve and use a geometric formula

2A b

h=

= 2(64.4) 14

= 9.2 Simplify.

ANSWER The height of the triangle is 9.2 meters.

h2A b=

PRACTICE

3. Write 5x + 4y = 20 so that y is a function of x.

54

y = 5 – x ANSWER

PRACTICE

The perimeter P of a rectangle is given by the formula P = 2l + 2w where l is the length and w is the width.

a. Solve the formula for the width w.

4 .

w = or w = – lP – 2l

2ANSWER

P2

PRACTICE

Use the rewritten formula to find the width of the rectangle shown.

b .

2.4ANSWER

How toHow to

page 170

PracticePractice

Pages 171-173

HomeworkHomework