Problem Set B: For #1 and #2, solve the equation using the guide of the boxes, then confirm that your solution is correct using the graph provided. 1. Solve xl - 2 = 3x + 2 2. S…

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asked Aug 5, 2023 60.0k views

1 Answer

Lukas Risko · Answer 1 · 2023-08-10T02:03:49+0000

Question 1:

Adding 2 to both sides of the equation gives

Now, the absolute value decomposes the above equation into two separate equations

$\begin{gathered} x=3x+4 \\ x=-3x-4 \end{gathered}$

The first equation gives

$\begin{gathered} x=3x+4 \\ -2x=4 \\ \boxed{x=-2} \end{gathered}$

The second equation gives

$\begin{gathered} x=-3x-4 \\ 4x=-4 \\ \boxed{x=-1} \end{gathered}$

The graph of the system is

We see that the solutions exists at x =-1.

Question 2.

Adding 2 to both sides of the equation gives

Decomposing the absolute value on LHS gives us two equations

$\begin{gathered} -(2x-1)=-x+2 \\ 2x-1=-x+2 \end{gathered}$

Solving the first equation gives

$\begin{gathered} 2x-1=x-2 \\ x=-1 \end{gathered}$

Solving the second equation gives

$\begin{gathered} 2x-1=-x+2 \\ 3x=3 \\ x=1 \end{gathered}$

Hence, the solution to the equation is

$x=\pm1$

The graph of the solutions is

We see that the solution is at x = -1 and x = 1; hence, our solution is confirmed.