Question

$x < 4$ is the solution set of $x + 6 < 10$. graph the solution set.

Explanation:

Step1: Analyze the inequality

The solution set is \( x < 4 \). For graphing inequalities on a number line:

• If the inequality is \( < \) or \( > \), we use an open circle at the boundary point (since the point is not included in the solution set).
• If the inequality is \( \leq \) or \( \geq \), we use a closed circle.

Here, the boundary point is \( 4 \), and since the inequality is \( x < 4 \), we use an open circle at \( 4 \).

Step2: Determine the direction of the line

Since \( x \) is less than \( 4 \), we shade the region to the left of \( 4 \) on the number line.

Graph Description:

• Place an open circle at \( 4 \) (because \( 4 \) is not included in \( x < 4 \)).
• Draw a line with an arrow pointing to the left (towards negative infinity) starting from the open circle at \( 4 \) to represent all numbers less than \( 4 \).

(Visually, on the given number line, the open circle should be at \( 4 \), and the line should extend to the left from \( 4 \), covering all numbers like \( 3, 2, 1, 0, -1, \dots \))

Answer:

Step1: Analyze the inequality

The solution set is \( x < 4 \). For graphing inequalities on a number line:

• If the inequality is \( < \) or \( > \), we use an open circle at the boundary point (since the point is not included in the solution set).
• If the inequality is \( \leq \) or \( \geq \), we use a closed circle.

Here, the boundary point is \( 4 \), and since the inequality is \( x < 4 \), we use an open circle at \( 4 \).

Step2: Determine the direction of the line

Since \( x \) is less than \( 4 \), we shade the region to the left of \( 4 \) on the number line.

Graph Description:

• Place an open circle at \( 4 \) (because \( 4 \) is not included in \( x < 4 \)).
• Draw a line with an arrow pointing to the left (towards negative infinity) starting from the open circle at \( 4 \) to represent all numbers less than \( 4 \).

(Visually, on the given number line, the open circle should be at \( 4 \), and the line should extend to the left from \( 4 \), covering all numbers like \( 3, 2, 1, 0, -1, \dots \))