Question

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

Part A: Determine two values that make the equation false. (2 points)

Part B: Explain why your integer solutions are false. Show all work. (2 points)

Answer 1

Is 47.5

Step-by-step explanation:

Answer 2

Values that make the equation 13 = 2x + 5 false include x=1 and x=0, as substituting these values results in 13 = 7 and 13 = 5, respectively, which are both false statements since they do not equate to 13.

Step-by-step explanation:

Part A: Finding Values That Make the Equation False

To find values that make the equation 13 = 2x + 5 false, we simply need to pick values of x that do not satisfy the equation. For example:

• If we substitute x with 1, the equation becomes 13 = 2(1) + 5, which simplifies to 13 = 7. This is false because 13 does not equal 7.
• If we substitute x with 4, the equation becomes 13 = 2(4) + 5, which simplifies to 13 = 13. Although this seems true, it's important to check our starting statement which requires a false solution. Hence, this value actually satisfies the equation and therefore is not what is being requested.
• If we substitute x with 0, the equation becomes 13 = 2(0) + 5, which simplifies to 13 = 5. This is false because 13 does not equal 5.

Part B: Explanation of False Solutions

The values of x provided (1 and 0) are false solutions because when we substitute them into the equation, the resulting expressions do not equal 13, which is what the equation 13 = 2x + 5 implies when it's true. Substituting x with 1 gives us 13 = 7, which is a false statement, and substituting with 0 gives us 13 = 5, which is also false. Both of them do not satisfy the original equation, making them incorrect solutions.