Math  /  Algebra

QuestionQ2) Which number line graphs the inequality 5x5 \geq x ? * Option 1 Option 2

Studdy Solution

STEP 1

1. We need to graph the inequality 5x5 \geq x.
2. The inequality 5x5 \geq x can also be written as x5x \leq 5.
3. We have two options to choose from, each representing a different graph of the inequality.

STEP 2

1. Understand the inequality and its implications.
2. Determine the correct representation of the inequality on a number line.
3. Choose the correct option based on the understanding.

STEP 3

The inequality 5x5 \geq x means that xx can be any number less than or equal to 5.

STEP 4

For x5x \leq 5, the number line should include all numbers to the left of 5, and since 5 is included in the solution (because of the "equal to" part), it should be represented with a closed circle at 5.

STEP 5

Compare the options: - Option 1 has an open circle at 5, which does not include 5 in the solution. - Option 2 has a closed circle at 5, which includes 5 in the solution.
The correct option is Option 2, as it accurately represents the inequality x5x \leq 5 with a closed circle at 5 and a red line extending to the left.
The correct number line graph for the inequality 5x5 \geq x is:
Option 2 \text{Option 2}

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