Question

Solve the inequality $-4(x + 4) > x + 7.$ Give your answer as an interval.

Answer 1

Answer:

$(-\infty,-4.6)$

Step-by-step explanation:

So we have the inequality:

$-4(x+4)>x+7$

First, let's distribute the left:

$-4x-16>x+7$

Now, let's add 16 to both sides:

$-4x>x+23$

Subtract x from both sides:

$-5x>23$

Divide both sides by -5. Since we're dividing by a negative, flip the sign:

$x<-4.6$

This is saying all values less than -4.6.

In other words, in an interval, this would be from negative infinity all the way up to -4.6. Thus:

$(-\infty,-4.6)$

We do not use brackets because we do not include -4.6 into our set.

And we're done!