Consider the equation 7x − 6 + 3 = 5x + 2x + 5.

Question

Question 1
Which BEST describes the number of solutions for the given equation?
Responses
A one solutionone solution
B two solutionstwo solutions
C infinitely many solutionsinfinitely many solutions
D no solution

Answer 1

To solve the equation $7x-6+3=5x+2x+5$, we start by simplifying both sides.

First, simplify the left side: $$7x-6+3=7x-3$$

Now simplify the right side: $$5x+2x+5=7x+5$$

Now the equation looks like this: $$7x-3=7x+5$$

Next, subtract $7x$ from both sides: $$-3=5$$

This statement is false, indicating that there is no value of $x$ that can satisfy the equation. Therefore, there are no solutions to the equation.

The BEST description of the number of solutions for the given equation is:

D. no solution