Question

Solve the compound inequality 3x + 4 > 5 and x – 2 < 7. Clearly show and explain each step please:)

Answer 1

Solve the inequality \(3x + 4 > 5 \) to start with.

Answer 2

I have this so far but I don't know how to explain where I combine them.

First we start by solving 3x + 4 > 5.
3x + 4 > 5 We subtract 4 from each side.
3x + 4 (-4) > 5 (-4) From here we get:
3x > 1 Now we divide 3 by each side.
3x/3 > 1/3 and we get:
x > 1/3
Now we solve for x – 2 < 7.
x – 2 < 7 We start by adding 2 to each side
x – 2 (+2) < 7 (+2) And from here we get:
x < 9

Answer 3

( @ParthKohli )

Answer 4

Here's how you combine:

For example, \(x > 1\) and \(9 > x\). Then \(9>x>1\)

Answer 5

Oh okay. Also, if most of the other solutions in my assignment finish with a solution looking like this? (for example) {x | x > -20}

with the x | ??