Question

solve the equation |4x−3|=5√(x+4)

Answer 1

please help solve it graphically and algebraically

Answer 2

Establish first and foremost, that x + 4 >= 0 or x >= -4

After that, just square both sides and see if anything helpful occurs.

Answer 3

@tkhunny ok but then how do you solve it graphically?

Answer 4

What did you get for the algebraic solution?

Answer 5

@tkhunny I got x= 3.86 and x=-0.79... is that what you got?

Answer 6

That's no good. You'll have to give that another go. Show me your intermediate results. Let's see where you wandered off.

Answer 7

@tkhunny wait no i divided wrong i think it should be 4.365 and -1.303

Answer 8

That's better. Off to graphing.

First, the absolute values:

Graph this line: y = 4x - 3
Graph this line: y = 3 - 4x

When you have that, let me know.

Answer 9

@tkhunny ok then what?

Answer 10

Erase everything where y < 0. It's an absolute value. We can't have a negative result!

Answer 11

ok so then that is the final answer? @tkhunny

Answer 12

Hold on there! You must also erase everything for x < -4. We said the up front, right?

Answer 13

oh yeah i forgot about that part

Answer 14

Should look something like this.

Answer 15

oh ok! thank you so much!!!

Answer 16

See how wonderfully that method just found the turning point for us? Very handy.

Okay, now the square root. Graph \(y = 5\sqrt{x+4}\)

For x = -4, we have y = 0
For x = 0, we have y = 10
Pick some other easy ones and start to get an idea how it goes.
For x = -3, what have we?

Answer 17

5?

Answer 18

Can you draw the graph, now, or do you need more points?

Answer 19

i think i can draw it now... but i just dont get how the two seprate graphs come together to make one graph?

Answer 20

Keep in mind that y = 3 - 4x has y-intercept 3, so this curve is quite a bit higher when hitting they-axis. Also, keep in mind the two intersections we already know. This will contribute to a better drawing.