Question

Solve |2x – 9| + 4 < 7. You must show all work. Use >= and <= to represent the inequalities. Use complete sentences to describe the graph in words

Answer 1

Start by isolating the absolute value:
\[|2x-9|<3\]
Now we'll use what we know about absolute value functions to turn this into a piecewise function. Write the two pieces and temporarily convert them into equations.

\[2x-9=3\]
and

\[-2x+9=3\]
From these we get intersections at x=3 and 6. From here, we test intervals between these points in the original inequality. We'll start with x < 3. I pick zero because it makes it easy, but you can pick whatever you like.
\[|2(0)+9|=9\]
Greater than 3, so it's not in our answer. Now for 3 < x < 6. I'm picking -4.5 because it cancels the 9:
\[|2(-4.5)+9|=0\]
Less than 3, so it works! Now for the last interval. No really nice numbers here:
\[|2(10)+9|=19\]
So it's not in our answer. The only interval that worked is our answer:
\[3<x<6\]

Answer 2

Thank you so much c: