Section 4.2 - Solving Linear Equations Using Inverse Operations

Explanation
To solve the equation 3x + 5 = 10, the first inverse operation that should be applied is subtraction. This is because the equation involves addition of 5, so subtracting 5 from both sides will eliminate the constant term on one side and isolate the variable term. This allows for further simplification and solving for the value of x.

Explanation
To solve the equation 5x + 3 = 23, we need to isolate the variable x. We can do this by subtracting 3 from both sides of the equation, giving us 5x = 20. Then, we divide both sides of the equation by 5 to solve for x, which gives us x = 4.

Explanation
To solve the equation x/5 + 2 = 7, we need to isolate the variable x. First, we subtract 2 from both sides of the equation, which gives us x/5 = 5. Next, we multiply both sides of the equation by 5 to eliminate the fraction, resulting in x = 25. Therefore, the correct answer is x = 25.

Explanation
The equation (x/2 - 6 = 20) represents the given problem accurately. It states that "half of a number minus 6 is 20". By dividing the number x by 2 and then subtracting 6, we should get the result of 20.

Explanation
The equation C = 2.5p + 75 represents the cost, C, to rent the roller skating rink when p people attend. In this equation, the coefficient of p is 2.5, indicating that the cost increases by $2.5 for each additional person. By substituting p = 100 into the equation, we can calculate the cost. C = 2.5(100) + 75 = 250 + 75 = $325. Therefore, if 100 people attend, it will cost $325.

Explanation
The equation P=2L + 2W represents the perimeter of a rectangle, where P is the perimeter, L is the length, and W is the width. In this case, we are given that the perimeter of the playground is 500m and the length is 120m. By substituting these values into the equation, we can solve for the width. Plugging in P=500m and L=120m, we get 500m=2(120m) + 2W. Simplifying this equation, we have 500m=240m + 2W. Subtracting 240m from both sides, we get 260m=2W. Dividing both sides by 2, we find that the width of the playground is 130m.

Explanation
The equation C = 10 + 0.25m represents the cost, C of a cell phone bill if m minutes are used. To find the equation that represents a bill of $25, we substitute 25 for C in the equation. By substituting 25 for C, the equation becomes 25 = 10 + 0.25m. This equation represents a bill of $25.

Explanation
To solve the equation x/4 + 6 = 9, we need to isolate the variable x. We can start by subtracting 6 from both sides of the equation, which gives us x/4 = 3. To solve for x, we can multiply both sides of the equation by 4, resulting in x = 12. Therefore, the correct answer is x = 12.

Explanation
To solve the equation 5 - 3e = 15, we need to isolate the variable "e". The inverse operation of subtraction is addition, so the first step is to add 5 to both sides of the equation. This will cancel out the 5 on the left side, leaving us with -3e = 10. Now we can proceed to solve for "e" by dividing both sides by -3.

Explanation
To solve the equation (x - 3) / 5 = 10, we can start by multiplying both sides of the equation by 5 to eliminate the fraction. This gives us x - 3 = 50. Then, we can add 3 to both sides to isolate x, resulting in x = 53. Thus, the correct answer is x = 53.