Question

You are given the equation 13=2x+5 with no solution set.

a. Determine two values that make the equation false.

Answer 1

To find two values that make the equation false, we can solve the equation and substitute different values for x. For example, when x = 3 or x = 7, the equation 13 = 2x + 5 is false.

Step-by-step explanation:

To determine two values that make the equation 13 = 2x + 5 false, we need to find values of x that when substituted into the equation do not result in 13. Let's solve the equation:

13 = 2x + 5

Subtract 5 from both sides:

8 = 2x

Divide both sides by 2:

4 = x

So, when x = 4, the equation is true. To find two values that make the equation false, we can choose any two values that are not equal to 4. For example, if we replace x with 3:

13 = 2(3) + 5

13 = 6 + 5

13 = 11

This is false. Similarly, if we replace x with 7:

13 = 2(7) + 5

13 = 14 + 5

13 = 19

This is also false. Therefore, choosing x = 3 and x = 7 as examples, we have two values that make the equation 13 = 2x + 5 false.

Answer 2

To determine values that make the equation 13=2x+5 false, you can choose any value for x, perform the operation 2x + 5, and check if it equals 13. Examples of false values for x are 1 and 10.

Step-by-step explanation:

When you are given the equation 13=2x+5 and asked to determine two values that make the equation false, you are looking for any values of x that do not satisfy the equation. To make the equation false, choose a value for x and perform the operation on the right side of the equation (2x + 5). Compare the result to the left side of the equation (13). If they are not equal, then that value of x makes the equation false.

Example for Incorrect Value

For instance, if you choose x=1, the operation on the right side would be 2(1) + 5 = 7, which is clearly not equal to 13, making the equation false.

Another Example for Incorrect Value

Similarly, if you choose x=10, the operation would be 2(10) + 5 = 25, and since 25 is not equal to 13, the equation would also be false with this value of x.