Question

How many solutions does the following equation have?

−7x−10−15x=−22x+83
A. no solutions
B. exactly one solution
C. infinitely many solutions

Answer 1

The equation −7x−10−15x=−2x+83 simplifies to a contradiction (−10 = 0), which means there are no solutions to this equation. The correct answer is A. No solutions.

Step-by-step explanation:

The student is asking how many solutions there are to the equation −7x−10−15x=−2x+83. To solve this, we need to bring like terms together and simplify the equation.

First, combine the terms on the left side of the equation:

−7x − 15x = −2x

−22x − 10 = −2x

Now, add 22x to both sides of the equation to get:

−10 = 0

Since −10 does not equal 0, there are no solutions to this equation. The equation is actually a contradiction because no value of x can make the statement true. Therefore, the correct answer is A. No solutions.

The given equation is −7x − 10 − 15x = −2x + 83. Combining like terms on the left side results in −22x − 10 = −2x. Adding 22x to both sides leads to −10 = 0, which is a contradiction. Thus, there are no solutions, making option A (No solutions) correct.