Question

When solving -1/5 (x − 25) = 7, what is the correct sequence of operations? (5 points)

Answer 1

To solve the equation -1/5 (x - 25) = 7, we need to isolate the variable x.

Here's the correct sequence of operations:

1. Distribute the -1/5 to the terms inside the parentheses:

-1/5 * x - 1/5 * (-25) = 7

Simplifying this gives us:

-1/5 * x + 5 = 7

2. Next, we want to get rid of the constant term on the left side of the equation. To do this, subtract 5 from both sides:

-1/5 * x + 5 - 5 = 7 - 5

Simplifying this gives us:

-1/5 * x = 2

3. Now, we want to isolate the variable x. Since -1/5 is multiplying x, we can multiply both sides of the equation by the reciprocal of -1/5, which is -5/1:

(-1/5 * x) * (-5/1) = 2 * (-5/1)

Simplifying this gives us:

x = -10

Therefore, the solution to the equation -1/5 (x - 25) = 7 is x = -10.

Note: When multiplying or dividing an equation by a negative number, it's important to remember that the direction of the inequality sign should be reversed. However, in this case, we are solving for x, so there is no inequality involved.

Answer 2

-10

Explanation:

To solve the equation -1/5(x - 25) = 7, you need to perform a series of operations in the correct sequence. Here's a step-by-step guide:

1. Start by distributing the -1/5 to both terms inside the parentheses:

-1/5 * x + -1/5 * -25 = 7

This simplifies to:

-1/5x + 5 = 7

2. Next, isolate the term with x by subtracting 5 from both sides of the equation:

-1/5x + 5 - 5 = 7 - 5

This simplifies to:

-1/5x = 2

3. To get rid of the fraction, multiply both sides of the equation by the reciprocal of -1/5, which is -5/1 (or -5):

-5/1 * -1/5x = 2 * -5/1

This simplifies to:

x = -10

Therefore, the solution to the equation -1/5(x - 25) = 7 is x = -10.