Question

02.03]

Compare and Contrast: Two equations are listed below. Solve each equation and compare the solutions. Choose the statement that is true about both solutions. (2 points)

Equation 1 Equation 2
|5x + 6| = 41 |2x + 13| = 28

Answer 1

@dude

Answer 2

Similar to what we just did with the past problems lets do equation 1 first
\[|5x + 6| = 41\]
We know that x can equal
\[5x+6=-41\quad \quad \mathrm{or}\quad \:\quad \:5x+6=41\]
For the first equation we can subtract 6 on both sides
\[5x=-47\]
Then we divide by 5 on both sides
\[x=-\frac{47}{5}\]

Answer 3

For the second equation
\[5x+6=41\]
We also subtract 6 on both sides
\[5x=35\]
Then we divide by 5 on both sides
\[x=7\]

Answer 4

Now for equation 2
\[|2x + 13| = 28]\]
We know that x can equal
\[2x+13=-28\quad \quad \mathrm{or}\quad \:\quad \:2x+13=28\]
For the left equation
\[2x+13=-28\]
Subtract 13 on both sides
\[2x=-41\]
The we divide 2 on both sides
\[x=-\frac{41}{2}\]

Answer 5

For the right equation
\[2x+13=28\]
Subtract 13 from both sides
\[2x=15\]
Divide 2 on both sides
\[x=\frac{15}{2}\]

Answer 6

Equation 1 and Equation 2 have the same number of solutions

Answer 7

So the solutions for equation #1 are
\[x=−\frac{47}{5}, 7\]
For equation #2
\[x=−\frac{41}{2}, \frac{15}{2}\]

Answer 8

Yes, they do have the same number of solutions

Answer 9

yes

Answer 10

One difference would be that they do not intersect at the same points