Consider the equation 7x - 6 + 3 = 5x + 2x + 5.
Which BEST describes the number of solutions for the given equation?
A. one solution
B. two solutions
C. infinitely many solutions
D. no solution
To solve the given equation, we can start by combining like terms on both sides. This gives us 7x - 6 + 3 = 5x + 2x + 5.
Simplifying further, we get 7x - 3 = 7x + 5.
Next, we want to isolate the variable x on one side of the equation. We can do this by subtracting 7x from both sides:
-3 = 5.
We can see that -3 does not equal 5. Therefore, there is no solution to the given equation.
The answer is D. no solution.
To determine the number of solutions for the given equation, we need to simplify and solve for x.
Given equation: 7x - 6 + 3 = 5x + 2x + 5.
Step 1: Combine like terms on both sides of the equation.
7x - 3 = 7x + 5.
Step 2: Move variables to one side and constants to the other side to isolate x.
7x - 7x = 5 + 3.
Step 3: Simplify.
0 = 8.
Step 4: Analyze the result.
We can see that the equation simplifies to 0 = 8, which is not a true statement.
Since the equation is inconsistent, it implies that there are no values of x that satisfy the equation.
Therefore, the answer is D. no solution.
To determine the number of solutions for the given equation, we need to simplify and solve it. Let's break down the equation step by step.
First, let's combine like terms on both sides of the equation. On the left side of the equation, we have 7x - 6 + 3, which simplifies to 7x - 3. On the right side of the equation, we have 5x + 2x + 5, which simplifies to 7x + 5.
After simplifying, the equation becomes:
7x - 3 = 7x + 5
Next, let's isolate the variable. We want to get all the x terms on one side of the equation and the constant terms on the other side. We can do this by subtracting 7x from both sides of the equation:
7x - 7x - 3 = 7x - 7x + 5
This simplifies to:
-3 = 5
Since -3 is not equal to 5, we have a contradiction. This means that there are no values of x that satisfy the equation. In other words, there is no solution to the equation.
Therefore, the correct answer is D. no solution.