Graph on a number line. |3x|≥ 21

Expert Answers
justaguide eNotes educator| Certified Educator

`|3x| >= 21` has to be graphed on a number line.

The absolute value of a number a, |a| = a if a >= 0 and -a if a < 0.

`|3x| >= 21`

=> `|x| >= 7`

=> `x >= 7` or `x <= -7`

On the number line this can be graphed as:

cgrant2 | Student

1. There is an absolute value on 3x meaning that we must consider the values the distance away from zero (positive and negative value). We need to solve the equation first. 

2. We need to solve for x, so we treat the inequality sign like an equal sign 

3x = 21 

x = 7 

In terms of absolute value, we know that x exists anywhere from -7 to 7. 

3. Now have to figure out the inequality. We know that the sign is greater than or equal to 7 so 7 is included in the set of number. To denote this, there is an closed circle at 7 

The values are: `x <= -7 and x>= 7`

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