List the integral values of which satisfy the inequality -2 < 7 – 3x ≤ 10

Answer 1

To solve the inequality \(-2 < 7 - 3x \leq 10\), we can break it into two parts and solve each part separately.

1. Solving the first part:

\[ -2 < 7 - 3x \]

Subtract \(7\) from both sides:

\[ -2 - 7 < -3x \quad \Rightarrow \quad -9 < -3x \]

Now, divide both sides by \(-3\). Remember that dividing by a negative number reverses the inequality:

\[ \frac{-9}{-3} > x \quad \Rightarrow \quad 3 > x \quad \Rightarrow \quad x < 3 \]

2. Solving the second part:

\[ 7 - 3x \leq 10 \]

Subtract \(7\) from both sides:

\[ -3x \leq 10 - 7 \quad \Rightarrow \quad -3x \leq 3 \]

Now, divide both sides by \(-3\) (again, reversing the inequality):

\[ x \geq \frac{3}{-3} \quad \Rightarrow \quad x \geq -1 \]

3. Combining the results from both parts, we have:

\[ -1 \leq x < 3 \]

This means the integral values of \(x\) that satisfy the compound inequality are \(-1, 0, 1, 2\).

Thus, the integral values that satisfy the inequality \(-2 < 7 - 3x \leq 10\) are:

\(-1, 0, 1, 2\)