Question

Solve for x: |x + 2| + 16 = 14

x = −32 and x = −4

x = −4 and x = 0

x = 0 and x = 28

No solution

Answer 1

What is the very first step you did to solve this?

Answer 2

You would plugin the values they give for x to see if one works

Answer 3

:: sigh :: I despise multiple choice questions. :p
Yes, that is one way of going about it.

But if you wish to understand this problem, it would be helpful to graph it and then go through the algebraic steps to understand why the solution works.

Answer 4

ok

Answer 5

go to https://www.desmos.com/calculator

and type these two equations, then zoom out until you see the functions.

y = abs(x+2) + 16
y = 14

Answer 6

I just did

Answer 7

Do the lines intersect?

Answer 8

yes

Answer 9

To solve

abs(x+2) + 16 = 14 subtract 16 from both sides
abs(x+2) = -2

NO SOLUTION!

The absolute value of ANYTHING is always 0 or greater.

So the absolute value of (x+2) will always be 0 or greater. There's NO WAY for it to be -2.

So that's that. :)

For fun, try typing in

y = a*abs(x+b) + c

and then press enter, then click "all".

Answer 10

i did

Answer 11

Click the sliders around to see what a,b, and c do to the graph. :)

Answer 12

i did

Answer 13

You can do that with any graph. Like

y = a*x^2+b*x+c
y = a*sin(b*x +c) + d
y = a*sqrt(b*x+c) + d
etc.

Answer 14

oh ok