Two Absolute Value problems.

[Red888]

These two have caught me out. One because its a multiplication of absolute values and the other because its a a graph, but...

 

Numbers: 3D and 4

 

Any help would be very much appreciated, thank you.

 

 

[hotcommodity]

You want to treat part 3d. as if there were absolute value bars outside of both sums being multiplied. So you would have | (x-1)*(x+2) | = 3. Now you can just multiply the two terms and get |x^2 +2x -x -2 |=3, now just add like-terms and solve. For part 4, one way to sketch a graph would be to simply plot points on an x-y graph. Start by picking whole numbers of x, both negative and positive and close to 0, 0 included. Remember if you get a negative value in the absolute value bars to simply make it positive. The line you graph should never go below the x-axis. I hope that helps.

[Red888]

Thank you very much. I appreciate your imput.

[Ramsey2879]

You want to treat part 3d. as if there were absolute value bars outside of both sums being multiplied. So you would have | (x-1)*(x+2) | = 3. Now you can just multiply the two terms and get |x^2 +2x -x -2 |=3, now just add like-terms and solve.

You can also solve if you substitute a+b for x and set a-1 = -(a+2). This gives a = -1/2. So (-3/2 + b)*(3/2+b) = +/- 3 gives b = +/-sqrt{21/4} since x is real. x = a+b = (-1+/-sqrt{21})/2