# Algebra: Equations Problems

The techniques for solving linear equations and linear inequalities are similar, yet different. Explain and give an example of both a linear equation and a linear inequality that demonstrates this difference.

1.) Solve and check the linear equation.

5x - 5 = 30

A) {30}

B) {34}

C) {11}

D) {7}

2.) Solve and check the linear equation.

9x - (7x - 1) = 2

A)

B)

C)

D)

3.) Solve and check the linear equation.

7x - 9 = -10 + 4x

A)

B)

C)

D)

4.) Solve and check the linear equation.

(-5x + 4) - 5 = -4(x - 7)

A) {19}

B) {- 6}

C) {29}

D) {- 29}

5.) Solve and check the linear equation.

-3x + 5 + 6(x + 1) = -2x + 3

A)

B)

C)

D)

6.) Solve and check the linear equation.

6[-6x + 6 + 4(x + 1)] = 6x + 2

A)

B)

C)

D)

7.) Solve and check the linear equation.

32 - 2(11 - 8)2 = 36x

A)

B) {4}

C)

D) {0}

8.) Solve and check the linear equation.

0.30(80) + 0.60x = 0.40(80 + x)

A) {20}

B) {30}

C) {50}

D) {40}

9.) Solve and check the linear equation.

0.40x - 0.20(50 + x) = -0.04(50)

A) {50}

B) {30}

C) {40}

D) {20}

10.) Solve the formula for the specified variable.

F = C + 32for C

A) C = (F - 32)

B) C =

C) C =

D) C = (F - 32)

11.) Solve the formula for the specified variable.

A = h(a + b)for a

A) a =

B) a =

C) a =

D) a =

12.) Solve the formula for the specified variable.

d = rtfor r

A) r = dt

B) r = d - t

C) r =

D) r =

13.) Solve the equation by factoring.

x2 = x + 6

A) {-2, -3}

B) {1, 6}

C) {-2, 3}

D) {2, 3}

14.) Solve the equation by factoring.

x2 + 2x - 120 = 0

A) {12, 10}

B) {12, -10}

C) {-12, 10}

D) {-12, 1}

15.) Solve the equation by factoring.

15x2 + 26x + 8 = 0

A)

B)

C)

D)

16.) Solve the equation by factoring.

2x2 - 15x = 8

A) {-2, 8}

B)

C)

D)

17.) Solve the equation by factoring.

11x2 - 9x = 0

A)

B)

C) {0}

D)

18.) Solve the equation by factoring.

3x(x - 5) = 7x2 - 16x

A)

B) {0}

C) {0, 4}

D)

19.) Solve the equation by factoring.

7 - 7x = (4x + 9)(x - 1)

A)

B) {-4, 1}

C)

D) {-1, 4}

20.) Solve the equation by factoring.

-6x - 2 = (3x + 1)2

A)

B)

C)

D)

https://brainmass.com/math/linear-algebra/algebra-equations-problems-466592

#### Solution Summary

This posting contains the answer to the given questions.

40 Algebra Problems : Solving Equations, Percentages, Writing Equations from Word Problems and Simplifying Expressions

Page 71 & 72

# 27 0.5 = -2.5 + x # 28 0.6 = - 1.2 + x #52 2 4x

-- = --

3 3

# 57 1

--y = -- --

3

# 91 Cigarette consumption. In 1999, cigarette consumption in the U. S. was 125 packs per capita. This rate of consumption was 5/8 of what it was in 1980. Fine the rate of consumption in 1980.

Page 77 & 78

# 15 2 # 16 1 #37 3x -3 = x + 5

-- x + 8 = 0 -- --z - 5 = 0

3 7

# 38 9y - 1 = 6y + 5

# 93 Celsius temperatures. If the air temperature in Quebec is 68* Fahrenheit, then the solution to the equation 9/5C + 32 = 68 gives the Celsius temperature of the air. Find the Celsius temperature.

Page 84 & 85

# 34 3m m #35 1 1 #49 0.05y + 0.03(y + 50) =17.5

--- + --- = 5 --p --5 = ---p

4 2 3 4

#50 0.07y + 0.08 (y - 100) = 44.5 #67 - 3x + 1 = --1 - 2x

#73 23 - 5 (3 - n ) = -- 4 (n -2 ) + 9n # 79 y y

-- + -- = 20

2 6

# 80 3w w

---- --1 = --- + 1

5 2

# 87 Sale commission. Danielle sold her house through an agent who charged 8% of the selling price after the commission was paid, Danielle received $ 117.760. if x is the selling price, then x satisfies

X - 0.08x = 117,760.

Solve this equation to find the selling price.

Page 91 & 92

# 30 2(x - 3w ) = --3 (x + w ) # 32 x - a = -- x + a + 4b

# 69 finding the original price. Find the original price if there is a 15% discount and the sale price is $ 255.

Page 99

Translate each verbal expression into an algebraic expression.

# 11 The product of a number and 5

# 12 Five divided by some number

# 13 Ten percent of a number

# 20 Write an algebraic expression for a pair of numbers Example.

Two numbers that differ by 9

Page 101

Write an algebraic expression for the following unknown integers.

# 77 The sum of three consecutive integers is 42

# 78 The sum of three consecutive odd integers is 27

# 91 Target he4art rate for cardiovascular work out, fitness experts recommend that you reach your target heart rate and stay at that rate for at least 20 minutes (Cycling, Burkett and Darst). To find your target rate, find the sum of your age and your resting heart rate, then subtract that sum from 220. Find 60 % of that result and add it to your resting heart rate.

A) Write an equation with variable r expressing the fact that the target heart rate for 30-year old is 144.

B) Judging from the accompanying graph, dose the target heart rate for

A 30-year old increase or decrease as the resting heart rate increases.

Page 106 & 107

Show a complete solution to each problem. Example

# 15 Framed. Julia framed an oil painting that her uncle gave her, the

Her uncle gave her. The painting was 4 inches longer than it

Was wide, and it took 176 inches of frame molding. What were

The dimension of the picture?

#18 Border paper. Dr. Good's waiting room is 8 feet longer than it is

Wide. When vicent wallpaper Dr. Good`s waiting room, he used 88

Feet of border paper. What are the dimensions of Dr. Good`s waiting

Room?

# 22 Walking and running. On Sunday morning, lynn walked for 2 hours

And then ran for 30 minutes. If she ran twice as fast as she walked

And she covered 12 miles al-together, then how fast did she walk?

# 25 Head winds. A jet flew at an average speed of 640 mp from os Angeles

To Chicago. Because of head winds the jet average only 512 mph on

The return trip, and the return trip took 48 minutes longer, how many

Hours was the flight from Chicago to Los Angeles? How far is it from

Chicago to Los Angeles?

Page 139 & 141

Determine whether -4 satisfies each compound inequality

# 17 2x -1 < --7 or -2x > 18

# 18 -- 3x > 0 and 3x - 4 < 11

# 78 3 < 5 - x < 8 or -3x < 0

# 79 --1 < 3x + 2 < 5 or 3/2x - 6 > 9

Solve this problem by using a compound inequality

# 85 keep on truck. Abdul is shopping for a new truck in a city with an 8%

Sale tax. There is also an $ 84 title and license fee to pay. He wants to get

A good truck and plans to spend at least $ 12,000 but no more than

$ 15,000. what is the price range for the truck ?

Page 148

# 26 [ x ] - 10 = -- 3 # 29 [ 3 -2x]

5 -- --------- = 4

3

# 33 [ 5 ] [ x ]

[ -- -- x] = [ 2 -- -- ]

2 2