How would you graph 2|3x-2|-6=-4 if the solution is x=1

Expert Answers

An illustration of the letter 'A' in a speech bubbles

(1) You can graph both `y=2|3x-2|-6` and `y=-4` and find the intersections.

The graph of y=-4 is a horizontal line.

The graph of `y=2|3x-2|-6` is a "V", opening up. Rewriting as:

`y=2|3(x-2/3)|-6=6|x-2/3|-6` we can see that the vertex is at `(2/3,-6)` and the slopes of the sides are `+-6`

The graphs:

From the graph we see that there are two solutions: `x=1/3,x=1`

This can be verified algebraically:






(2) Or you can rewrite the equation so it is equal to zero and graph to find the x-intercepts:



Graph `y=2|3x-2|-2` ;

Again we see that the solutions (here the x-intercepts) are `x=1/3,x=1`

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial