Question

YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT 11) Decide if each equation has no solution or infinitely many solutions (all real numbers). 2 pts ea. a) 2(x + 1) = 2x + 2 b) 8x - 7 = 8(x + 1) c) X-3 = x + 17

Answer 1

`\begin{gathered} a)\text{ Infinitely many solutions.} \\ b)\text{ No solutions.} \\ c)\text{ Infinitely many solutions.} \end{gathered}`

Step by step explanation:

To determine if each equation has no solution or infinitely many solutions, we need to solve for x and see if we get 0=0, which means the equation has infinitely many solutions, and if we get a false statement like 5=8 that means the equation does not have a solution.

Then, for a).

`\begin{gathered} 2(x+1)=2x+2 \\ 2x+2=2x+2 \\ 0=0\rightarrow\text{ Infinitely many solutions} \end{gathered}`

For b)

`\begin{gathered} 8x-7=8(x+1) \\ 8x-7=8x+8 \\ 8x-8x=8+7 \\ 0=15 \\ \text{ The equation does not have a solution.} \end{gathered}`

For c)

`\begin{gathered} x-3=x+17 \\ x-x=17+3 \\ 0=20 \\ \text{ Infinitely many solutions.} \end{gathered}`