Question

one-step inequalities

solve each inequality and graph its solution.

1. -7x > 21

1. n - 6 \le -14

Explanation:

Solve the first inequality

Using the Linear Inequalities knowledge point:
The first inequality is printed backwards or misaligned as:

$$ -7x > 21 $$

Divide both sides by \(-7\) and reverse the inequality sign:

$$ x < -3 $$

Graph the first solution

Using the Number Line Representation knowledge point:

• Place an open circle at \(-3\).
• Draw an arrow pointing to the left.

Solve the second inequality

Using the Linear Inequalities knowledge point:
The second inequality is:

$$ n - 6 \le -14 $$

Add \(6\) to both sides:

$$ n \le -8 $$

Graph the second solution

Using the Number Line Representation knowledge point:

• Place a closed circle at \(-8\).
• Draw an arrow pointing to the left.

Answer:

Question 1

The solution is:

$$ x < -3 $$

Question 3

The solution is:

$$ n \le -8 $$