Page 21 - 091math-wb-w6-(equations&inequalities-1)

Workbook

EQUATIONS and INEQUALITIES INVOLVING ABSOLUTE VALUE

Translating to an Absolute Value Expression

➢ Absolute value expressions can be used to describe distances. The distance between c and d is given
by c d . For example, the distance between -2 and 3 on the number line is   2  3  as
5
expected.

Example 1: Write the following sentences as an algebraic expression involving an absolute value.

a) Distance between x and 3.

b) Distance between x and -5.

c) Distance between x and 2 is 5.

d) Distance of a number to -10 is 7.

Example 2: Write an absolute value inequality to represent the following phrases.

a) All real numbers x, whose distance from zero is greater than 5 units.

b) All real numbers x, whose distance from -7 is less than 3 units.

c) All real numbers x, whose distance from 5 is between 1 and 4.

NOTE: Absolute value expressions can also be used to describe boundaries for measurement error.

Example 3: Deniz measured a certain compound on a scale in the chemistry lab at school. She
measured 8 gram of the compound, but the scale is only accurate to 0,1g . Write an absolute value

inequality to express an interval for the true mass, x, of the compound she measured.

21 091math-wb-w6-(equations&inequalities-1)