Question

If a number x must meet the two conditions below, which graph represents possible values for x? • Twice x is at least 18, and . Three less than x is greater than 10

Answer 1

A) x > 13

Explanation:

Given conditions:

• Twice x is at least 18, and
• Three less than x is greater than 10

Break down the conditions one by one.

Condition 1

"Twice x is at least 18" can be expressed as 2x ≥ 18.

This can be simplified by dividing both sides of the inequality by 2, which gives:

• x ≥ 9

Condition 2

"Three less than x is greater than 10" can be expressed as x - 3 > 10.

This can be simplified by add 3 to both sides of the inequality, which gives:

• x > 13

Solution

We need to find the values of x that satisfy both conditions.

So, x must be greater than or equal to 9 (from condition 1) and greater than 13 (from condition 2). This means x must be greater than 13, as the condition x ≥ 9 is already met when x > 13.

Graphing

When graphing inequalities on a number line:

• A closed circle (solid dot) is used to represent that a particular value is included in the solution set. This is used when the inequality sign is ≤ or ≥.
• An open circle (empty dot) is used to represent that a particular value is not included in the solution set. This is used when the inequality sign is < or >.
• For ≤ or <, shade to the left of the point on the number line.
• For ≥ or >, shade to the right of the point on the number line

Therefore, to graph x > 13 on a number line, place an open circle at 13 and shade to the right of the circle.