absolute value

Express the fact that x differs from 3 by less than 2/7 as an inequality involving absolute value. Solve for x. Let's build this algebraic expression in pieces: The phrase differs from means a difference. x - 3 By less than 2/7 means we use the < sign compared to 2/7 x - 3 < 2/7 Finally...

which number is the same distance from 0 on the number line as 4 We use absolute value for distance. Since 4 is 4 units right of 0 on the number line, we can also move 4 units left of 0 on the number line and we land on -4

Find all numbers who’s absolute value is 7 We have 2 numbers with an absolute value of 7: 7 since |7| = 7 -7 since |-7| = 7

Find all numbers whose absolute value is -3 None. Absolute values are always positive, so no number has a negative absolute value.

the absolute value of the difference 6 and k The difference of 6 and k means we subtract k from 6: 6 - k Take the absolute value: |6 - k|

19 decreased by the absolute value of c Take this algebraic expression in parts: Absolute value of c: |c| 19 decreased by the absolute value of c is found by subtracting |c| from 19 19 - |c|

find all numbers whose absolute value is 7 |7| = 7 |-7| = 7 So we have two numbers: (-7, 7)

the absolute value of a number is its _____ from 0 The answer is distance. As an example: 2 and -2 are 2 units away from 0.

distance between -2 and 9 on the number line Distance on the number line is the absolute value of the difference: D = |9 - -2| D = |11| D = 11

absolute value of x is less than or equal to 4 Absolute value of x: |x| Set up an inequality where this is less than or equal to 4: |x| <= 4 <-- This is our algebraic expression To solve this, we have the following compound inequality: -4 < x < 4

Find all numbers whose absolute value is 6. 2 numbers: |6| = 6 |-6| = 6

|(x-7)/5|<=4 Set up two equations: (x-7)/5 <= 4 (x-7)/5 > -4 Cross Multiply (1): x - 7 <= 20 Add 7 to each side: x <= 27 Cross Multiply (2): x - 7 > -20 Add 7 to each side: x > -13

What numbers have an absolute value of 9 9 since |9| = 9 -9 since |-9| = 9

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 120 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was...

Distance implies the positive difference between 2 points. Therefore, we use absolute value: |x - 8| < 14 Note, we use less than since 14 is not included.

Subtract 5 from each side: -8|-2n| = -80 Divide each side by -8 |-2n| = 10 Since this is an absolute value equation, we need to setup two equations: -2n = 10 -2n = -10 Solving for the first one by dividing each side by -2, we get: n = -5 Solving for the second one by dividing each side by...

Absolute value of x is denoted as |x|. Set that to less than 8, we have: |x| < 8