Question

1. solve and graph the inequality on a number line: 3x + 7 < 19 answer: ____________

Explanation:

Step1: Subtract 7 from both sides

To isolate the term with \( x \), we subtract 7 from both sides of the inequality \( 3x + 7 < 19 \). This gives us \( 3x + 7 - 7 < 19 - 7 \), which simplifies to \( 3x < 12 \).

Step2: Divide both sides by 3

To solve for \( x \), we divide both sides of the inequality \( 3x < 12 \) by 3. This gives us \( \frac{3x}{3} < \frac{12}{3} \), which simplifies to \( x < 4 \).

For graphing on a number line:

• Draw a number line.
• Place an open circle at 4 (since \( x \) is less than 4, not less than or equal to 4, so the point 4 is not included).
• Shade the region to the left of 4 to represent all values of \( x \) that satisfy the inequality.

Answer:

The solution to the inequality \( 3x + 7 < 19 \) is \( x < 4 \). For the graph, there is an open circle at 4 on the number line with shading to the left of 4.