Question

How do you solve compound inequalities `5a-4>16 or 3a + 2 <17`?

Answer 1

`a>4` or `a<5`

Explanation:

We have the following:

`color(limegreen)(5a-4>16)` and `color(blue)(3a+2<17)`

Let's start with our green inequality. We can add `4` to both sides to get

`color(limegreen)(5a>20)`

Next, divide both sides by `5` to get

`color(limegreen)(a>4)`

Next, let's look at our blue inequality. Let's subtract `2` from both sides to get

`color(blue)(3a<15)`

Lastly, let's divide bot hsides by `3` to get

`color(blue)(a<5)`

Our solutions are

`a>4` or `a<5`

Hope this helps!

Answer 2

`a>4` or `a<5`

Explanation:

1) Solving first inequality:

`5a-4>16`

`5a-4+4>16+4`

`5a>20`

`{5a}/5>20/5`

`a>4`

2) Solving second inequality:

`3a+2<17`

`3a+2-2<17-2`

`3a<15`

`{3a}/3<15/3`

`a<5`