Question

Solve for x.
–2<5x+3<13
Write your answer as a compound inequality with integers.

Answer 1

To solve the compound inequality \(-2 < 5x + 3 < 13\), you can break it into two separate inequalities:

1. \(-2 < 5x + 3\)
2. \(5x + 3 < 13\)

### Step 1: Solve the first inequality

1. \(-2 < 5x + 3\)

Subtract 3 from both sides:

\[
-2 - 3 < 5x
\]

\[
-5 < 5x
\]

Now, divide both sides by 5:

\[
-1 < x
\]

So, this simplifies to:

\[
x > -1
\]

### Step 2: Solve the second inequality

2. \(5x + 3 < 13\)

Subtract 3 from both sides:

\[
5x < 13 - 3
\]

\[
5x < 10
\]

Now, divide both sides by 5:

\[
x < 2
\]

### Step 3: Combine the results

Now we have two inequalities:

1. \(x > -1\)
2. \(x < 2\)

Putting this together, we can express the solution as a compound inequality:

\[
-1 < x < 2
\]

### Final Answer

The solution for \(x\) in the form of a compound inequality is:

\[
(-1, 2)
\]

If you want to express this in terms of integers, the integers that satisfy this inequality are:

\[
0, 1
\]

So, the integer solution can also be written as:

\[
x \in \{0, 1\}
\]