Question

Solve for w.
19>5w+14>4
Write your answer as a compound inequality with integers.

Answer 1

To solve the compound inequality \( 19 > 5w + 14 > 4 \), we can split it into two separate inequalities:

1. \( 19 > 5w + 14 \)
2. \( 5w + 14 > 4 \)

Let's solve the first inequality \( 19 > 5w + 14 \):

1. Subtract 14 from both sides:
\[
19 - 14 > 5w
\]
\[
5 > 5w
\]

2. Divide both sides by 5:
\[
1 > w \quad \text{or} \quad w < 1
\]

Now, let's solve the second inequality \( 5w + 14 > 4 \):

1. Subtract 14 from both sides:
\[
5w > 4 - 14
\]
\[
5w > -10
\]

2. Divide both sides by 5:
\[
w > -2
\]

Now we combine the two results:

\(-2 < w < 1\)

Thus, the solution as a compound inequality in integer form is:
\[
-2 < w < 1
\]

In integer form, this means:
\[
w \in \{-1, 0\}
\]

So the answer expressing the range as a compound inequality with integers is:

\(-2 < w < 1\), and the integers satisfying this are \(-1\) and \(0\).