# Section 4.1 - Interpreting The Solution Of A Linear Equation

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Interpreting the solution of a linear equation is a topic in algebra therefore if you are a student in need of practice then this quiz is for you. If you are prepared to test your knowledge try it out.

• 1.

### Solve 4x + 2 =18

• A.

X = 5

• B.

X = 4

• C.

X = 9

• D.

X = 16

B. X = 4
Explanation
To solve the equation 4x + 2 = 18, we need to isolate the variable x.
First, we subtract 2 from both sides of the equation to get 4x = 16.
Then, we divide both sides by 4 to solve for x, which gives us x = 4.
Therefore, the correct answer is x = 4.

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• 2.

### Estimate the solution to 6x + 2 = 5

• A.

X = 2

• B.

X = 5

• C.

X = 6

• D.

X = 1/2

D. X = 1/2
Explanation
To estimate the solution to the equation 6x + 2 = 5, we need to isolate the variable x. By subtracting 2 from both sides of the equation, we get 6x = 3. To solve for x, we divide both sides of the equation by 6, which gives us x = 1/2. Therefore, the correct answer is x = 1/2.

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• 3.

### Sophie is buying a gold chain.  The gold chain costs \$2.50 per cm.  How many cm can she buy if she has \$30 to spend?

• A.

30cm

• B.

250cm

• C.

12cm

• D.

6cm

C. 12cm
Explanation
Sophie has \$30 to spend and the gold chain costs \$2.50 per cm. To find out how many cm she can buy, we divide the total amount she has by the cost per cm. So, \$30 divided by \$2.50 equals 12. Therefore, Sophie can buy 12 cm of the gold chain with her \$30.

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• 4.

### A plumber charges a \$75 flat fee plus \$25 per hour for each job.  Which linear equation represents the cost of a job that lasts "t" hours?

• A.

C = 25t + 75

• B.

C = 75t + 25

• C.

C = 25t

• D.

C = 100t

A. C = 25t + 75
Explanation
The equation c = 25t + 75 represents the cost of a job that lasts "t" hours. The \$75 flat fee is added to the \$25 per hour charge for each hour of work. This equation follows the form of a linear equation, where the cost (c) is equal to the rate per hour (25t) multiplied by the number of hours (t), with the flat fee (75) added.

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• 5.

### Find the x-intercept of the equation y = 3x - 6

• A.

(0, -6)

• B.

(-6, 0)

• C.

(2, 0)

• D.

(0, 2)

C. (2, 0)
Explanation
The x-intercept of an equation is the point where the graph of the equation intersects the x-axis. To find the x-intercept, we set y = 0 and solve for x. In the given equation y = 3x - 6, when y = 0, we have 0 = 3x - 6. Solving this equation, we find x = 2. Therefore, the x-intercept is (2, 0).

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• 6.

### Which function will not have an x-intercept?

• A.

Y = x

• B.

Y = -2x

• C.

Y = 5

• D.

X = 2

C. Y = 5
Explanation
The equation y = 5 represents a horizontal line with a y-coordinate of 5. Since the line is parallel to the x-axis, it will never intersect the x-axis and therefore will not have an x-intercept.

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• 7.

### Nate is saving up to purchase a new computer.  He has \$175 already and can save \$20 per month.  How long will it take him to save \$515?

• A.

17 months

• B.

34 months

• C.

26 months

• D.

20 months

A. 17 months
Explanation
Nate already has \$175 and can save \$20 per month. To calculate how long it will take him to save \$515, we can subtract his current savings from the target amount and then divide it by his monthly savings. \$515 - \$175 = \$340. \$340 รท \$20 = 17. Therefore, it will take Nate 17 months to save \$515.

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• 8.

### Use algebra to solve the equation 4x + 3 = -13

• A.

X = -2.5

• B.

X = -16

• C.

X = -4

• D.

X = -3

C. X = -4
Explanation
To solve the equation 4x + 3 = -13, we need to isolate the variable x. First, we subtract 3 from both sides of the equation to get 4x = -16. Then, we divide both sides by 4 to solve for x. This gives us x = -4. Therefore, the correct answer is x = -4.

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• 9.

### Find the x-intercept of the equation y =  x + 3

• A.

(3, 0)

• B.

(0, 0)

• C.

(-3, 0)

• D.

(0, 3)

C. (-3, 0)
Explanation
The x-intercept of an equation represents the point where the graph of the equation intersects the x-axis. To find the x-intercept, we set y=0 and solve for x. In this equation, when y=0, x+3=0, which gives x=-3. Therefore, the x-intercept is (-3, 0).

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• 10.

### A cell-phone company charges \$10 per month plus \$0.10 per minute.  How many minutes can Tori use if she budgeted \$30 per month for her cell-phone bill?

• A.

2000 min

• B.

300 min

• C.

20 min

• D.

200 min

D. 200 min
Explanation
Tori has a budget of \$30 per month for her cell-phone bill. The cell-phone company charges \$10 per month plus \$0.10 per minute. To find out how many minutes Tori can use, we subtract the fixed monthly charge of \$10 from her budget, which leaves \$20. Then, we divide this remaining amount by the cost per minute, which is \$0.10. By doing this calculation, we find that Tori can use 200 minutes within her budget of \$30 per month.

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• Current Version
• Mar 20, 2023
Quiz Edited by
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• Oct 07, 2008
Quiz Created by
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