Section 4.1 - Interpreting The Solution Of A Linear Equation

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.

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.

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.

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.

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).

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.

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.

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.

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).

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.