Question

Write the absolute value of each of the following:

(i) 14
(ii) −25
(iii) 0
(iv) −125
(v) −248
(vi) a −7, if a is greater than 7
(vii) a −7, if a −2 is less than 7
(viii) a + 4, if a is greater than −4
(ix) a + 4, if a is less than −4
(x) $\left|-3\right|$
(xi) $-\left|-5\right|$
(xii) $\left|12-5\right|$

Answer 1

(i) Absolute value of 14 is 14.
(ii) Absolute value of −25 is 25.
(iii) Absolute value of 0 is 0.
(iv) Absolute value of −125 is 125.
(v) Absolute value of −248 is 248.
(vi) Absolute value of (a − 7) is (a − 7) if a is greater than 7, that is, a − 7 > 0.
(vii) if a − 2 is less than 7, that is, a − 2 < 7 ⇒ a < 9 or a − 7 < 2
So absolute value of a−7 = a−7 if 7 < a < 9 that is a−2 is less than 7 but a−2 is greater than 5.
and absolute value will be −(a−7) if a < 7 if a−7 is less than 5.
(viii) Absolute value of (a + 4) is (a + 4) if a is greater than −4, that is, a > −4 ⇒ a + 4 > 0.
(ix) Absolute value of (a + 4) is −(a + 4) if a is less than −4, that is, a < −4 ⇒ a + 4 < 0.
(x) Absolute value of −3 is 3.
(xi) −|−5| is −5 and its absolute value is 5.
(xii) |12 − 5 | = | 7| and its absolute value is 7.