Section 4.1 - Interpreting The Solution Of A Linear Equation

1. Solve 4x + 2 =18

X = 5

X = 4

X = 9

X = 16

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.

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.

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

X = 2

X = 5

X = 6

X = 1/2

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.

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.

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?

30cm

250cm

12cm

6cm

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.

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.

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?

C = 25t + 75

C = 75t + 25

C = 25t

C = 100t

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.

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.

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

X = -2.5

X = -16

X = -4

X = -3

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.

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.

6. 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?

17 months

34 months

26 months

20 months

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 ÷ $20 = 17. Therefore, it will take Nate 17 months to save $515.

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 ÷ $20 = 17. Therefore, it will take Nate 17 months to save $515.

7. Which function will not have an x-intercept?

Y = x

Y = -2x

Y = 5

X = 2

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.

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.

8. Find the x-intercept of the equation y = 3x - 6

(0, -6)

(-6, 0)

(2, 0)

(0, 2)

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).

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).

9. Find the x-intercept of the equation y = x + 3

(3, 0)

(0, 0)

(-3, 0)

(0, 3)

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).

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).

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?

2000 min

300 min

20 min

200 min

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.

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.