Question

lesson practice
a. determine which of the values {-2, 0, 5, 11} are part of the solution set of the inequality 3x + 4 < 19.
graph each inequality.
b. u > -2
c. t ≥ 2.5

Explanation:

Part a

Step 1: Solve the inequality

First, solve the inequality \(3x + 4<19\). Subtract 4 from both sides:
\(3x+4 - 4<19 - 4\)
\(3x<15\)
Then divide both sides by 3:
\(\frac{3x}{3}<\frac{15}{3}\)
\(x < 5\)

Step 2: Check each value

• For \(x=-2\): \(-2<5\), so \(-2\) is a solution.
• For \(x = 0\): \(0<5\), so \(0\) is a solution.
• For \(x = 5\): \(5 = 5\) (not less than 5), so \(5\) is not a solution.
• For \(x=11\): \(11>5\), so \(11\) is not a solution.

To graph \(u>-2\) on a number line:

1. Draw a number line.
2. Locate \(-2\) on the number line.
3. Since the inequality is \(u > - 2\) (not \(u\geq - 2\)), we use an open circle at \(-2\) to indicate that \(-2\) is not included in the solution set.
4. Draw an arrow to the right of \(-2\) to show all numbers greater than \(-2\).

To graph \(t\geq2.5\) on a number line:

1. Draw a number line.
2. Locate \(2.5\) on the number line.
3. Since the inequality is \(t\geq2.5\), we use a closed circle at \(2.5\) to indicate that \(2.5\) is included in the solution set.
4. Draw an arrow to the right of \(2.5\) to show all numbers greater than or equal to \(2.5\).

Answer:

The values \(-2\) and \(0\) are part of the solution set.

Part b