Questions: Use both the addition and multiplication properties of inequality to solve the inequality and graph the set on a number line. -5x-2<28 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type your answer in interval notation.) B. The solution set is , the empty set.

Solution Steps

To solve the inequality \(-5x - 2 < 28\), we will first use the addition property of inequality to isolate the term with \(x\) on one side. Then, we will use the multiplication property of inequality to solve for \(x\). Finally, we will express the solution in interval notation.

We start with the inequality:

\[ -5x - 2 < 28 \]

To isolate the variable \(x\), we first add 2 to both sides of the inequality:

\[ -5x - 2 + 2 < 28 + 2 \]

This simplifies to:

\[ -5x < 30 \]

Next, we divide both sides of the inequality by \(-5\). Remember, when dividing or multiplying both sides of an inequality by a negative number, the inequality sign must be reversed:

\[ x > \frac{30}{-5} \]

This simplifies to:

\[ x > -6 \]

The solution \(x > -6\) can be expressed in interval notation as:

\[ (-6, \infty) \]

To graph the solution on a number line, draw a number line and place an open circle at \(-6\) to indicate that \(-6\) is not included in the solution. Shade the line to the right of \(-6\) to represent all numbers greater than \(-6\).

Final Answer