# Linear Equations and Solving Equations

The function that relates weight in grams of a crystal (w) to the temperature t in degrees Fahrenheit in which it was grown is as follows (fictitious):

W(t) = 0.8t + 12 Find w(-6).

a. impossible to tell from info given

b. less than 8 grams

c. at least 8 grams but less than 10 grams

d. at least 10 grams but less than 12 grams

e. at least 12 grams

What is the equation that contains these two points? (-3, 8) and (4, -2)

a. impossible to tell from info given or NONE of the following

b. y = -1.4286 + 3.7143x

c. y = 1.4286x + 3.7143

d. y = -1.4286x + 3.7143

e. y = 1.4286 - 3.7143x

Evaluate for x = -3-2x + 8

a. impossible to tell from info given

b. a number less than 6

c. at least 6 but less than 12

d. at least 12 but less than 15

e. at least 15

What was the original price, if there was a 22% discount and you ended up paying $42.90?

a. impossible to tell from info given

b. a figure less than $54

c. at least $54 but less than $56

d. at least $56 but less than $58

e. at least $58

What was the percent increase, if your stock went from $88 to $110?

a. impossible to tell from info given

b. less than 25%

c. at least 25% but less than 28%

d. at least 28% but less than 33%

e. at least 33%

Solve for x: 2(x-3) + 8(4-x) = 38

a. impossible to tell from info given

b. a number less than -3

c. at least -3 but less than -1

d. at least -1 but less than +2

e. at least +2

Solve the system:

2x - 3y = 18

x + y = -1

a. impossible to tell from info given

b. none of the following

c. the system is inconsistent

d. the system is dependent

e. (3, -4)

Solve the system:

2x + 3y = 12

x + 1.5y = -1

a. impossible to tell from info given

b. none of the following

c. the system is inconsistent

d. the system is dependent

e. (3, -4)

What is the slope of the following line? 2x - 3y = 18

a. impossible to tell from info given

b. a number less than 1

c. at least 1 but less than 1.5

d. at least 1.5 but less than 2

e. at least 2

You have $61,000 in your budget for a techie. You must pay the techie's salary, plus a 19% of salary benefits package from your budget for the techie. What is the highest salary (to the nearest cent) that you can advertise for your techie and stay within budget?

a. impossible to tell from info given

b. a figure less than $50,000

c. at least $50,000 but less than $51,000

d. at least $51,000 but less than $52,000

e. at least $52,000

Al got 60% of the items correct on a test. He got 18 items correct. How many items were there on the test?

a. fewer than 30

b. at least 30 but fewer than 32

c. at least 32 but fewer than 34

d. at least 34 but fewer than 36

e. at least 36

Evaluate for a = -1:

a. impossible to tell from info given

b. a number less than 0

c. at least 0 but less than 2

d. at least 2 but less than 4

e. at least 4

Subtract: |8-7+2-4| - |3-6+2|

a. a number less than 0

b. 0

c. 1

d. 2

e. a number greater than 2

A rectangle is 5 feet longer than it is wide. The perimeter is 78 feet. What is its length?

a. impossible to tell from info given

b. a number less than 16

c. at least 16 ft but less than 18 ft

d. at least 18 ft but less than 20 ft

e. at least 20 ft

Evaluate by using decimal equivalents:

a. a figure less than -1.50

b. at least -1.50 but less than -1.00

c. at least -1.00 but less than -0.50

d. at least -0.50 but less than 0

e. at least 0

The fixed cost for a widget is $43, with a variable cost of $81. How much would it cost to produce 200 widgets?

a. less than $10,000

b. at least $10,00 but less than $15,000

c. at least $15,000 but less than $17,000

d. at least $17,000 but less than $20,000

e. at least $20,000

Which of the following datasets is a straight-line graph?

a. impossible to tell from info given

b. none of the following

c.

x y

4 5

5 3

7 2

d.

r t

66 330

29 145

41 205

e.

h k

450 230

348 266

590 110

(Direct variation) A 12-foot canoe weighs 170.4 lbs. How much does a 20-ft canoe weigh?

a. impossible to tell from info given

b. less than 280 lbs

c. at least 280 but less than 290 lbs

d. at least 290 but less than 300 lbs

e. at least 300 lbs

A line that is perpendicular to this equation would have what slope? Y = 0.2X - 3

a. impossible to tell from info given

b. less than -4.00

c. at least -4.00 but less than -1.00

d. at least -1.00 but less than 0

e. at least 0

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The function that relates weight in grams of a crystal (w) to the temperature t in degrees Fahrenheit in which it was grown is as follows (fictitious):

W(t) = 0.8t + 12 Find w(-6).

a. impossible to tell from info given

b. less than 8 grams

c. at least 8 grams but less than 10 grams

d. at least 10 grams but less than 12 grams

e. at least 12 grams

Substitute -6 for t in the weight equation

grams.

So the weight is less than 8 grams.

Answer: b

What is the equation that contains these two points? A(-3, 8) and B(4, -2)

a. impossible to tell from info given or NONE of the following

b. y = -1.4286 + 3.7143x

c. y = 1.4286x + 3.7143

d. y = -1.4286x + 3.7143

e. y = 1.4286 - 3.7143x

First find the slope:

If there is another arbitrary point (x, y) on the line, with A(-3, 8), the slope can be written as

Answer: D

Evaluate for x = -3-2x + 8

a. impossible to tell from info given

b. a number less than 6

c. at least 6 but less than 12

d. at least 12 but less than 15

e. at least 15

Solve the equation,

Answer: B

What was the original price, if there was a 22% discount and you ended up paying $42.90?

a. impossible to tell from info given

b. a figure less than $54

c. at least $54 but less than $56

d. at least $56 but less than $58

e. at least $58

Let the original price be x, then you actually paid

Answer: C

What was the percent increase, if your stock went from $88 to $110?

a. impossible to tell from info given

b. less than 25%

c. at least 25% but less than 28%

d. at least 28% but ...

#### Solution Summary

Nineteen problems regarding linear equations and solving equations are solved. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.