Find the range of values for x if `-7lt3-2xlt9.`

Answer

To solve the inequality \(-7 < 3 - 2x < 9\), we will break it down into steps.

### Step 1: Write down the inequality
We start with the given inequality:
\[ -7 < 3 - 2x < 9 \]

### Step 2: Isolate the term containing \(x\)
To isolate the term containing \(x\), we will subtract \(3\) from all parts of the inequality:
\[ -7 - 3 < 3 - 2x - 3 < 9 - 3 \]
This simplifies to:
\[ -10 < -2x < 6 \]

### Step 3: Divide by \(-2\)
Next, we need to eliminate the coefficient of \(x\), which is \(-2\). We will divide all parts of the inequality by \(-2\). Remember that dividing by a negative number reverses the inequality signs:
\[ \frac{-10}{-2} > \frac{-2x}{-2} > \frac{6}{-2} \]
This simplifies to:
\[ 5 > x > -3 \]
or equivalently,
\[ -3 < x < 5 \]

### Final Answer
The range of values for \(x\) is:
\[ -3 < x < 5 \]