how many solutions does the equation 2(b+3)-17=3b-7+b have?

Question

a. one soultion
b. infinity many soultions
c. two soultions
d.no soultions

Answer 1

To solve the equation \( 2(b + 3) - 17 = 3b - 7 + b \), let's simplify both sides step by step.

Starting with the left side: \[ 2(b + 3) - 17 = 2b + 6 - 17 = 2b - 11 \]

Now simplifying the right side: \[ 3b - 7 + b = 4b - 7 \]

Now we have the equation: \[ 2b - 11 = 4b - 7 \]

Next, let's rearrange the equation to isolate \( b \): \[ 2b - 4b = -7 + 11 \] \[ -2b = 4 \] \[ b = -2 \]

Since we found a unique value for \( b \), the equation has one solution.

Thus, the answer is: a. one solution