a. x = 6 OR x = - 4
b. x = 5
Explanation:
(a)
X² – 2x – 24 = 0
What two numbers that if we add them together will give us -2 but when multiplied give us – 24?
These are -6 and 4. Therefore;
X2 + 4x – 6x – 24 = 0
x(x + 4) – 6 (x + 4) = 0
(x - 6) (x + 4) = 0
X can therefore be
X – 6 = 0
X = 6
OR
X + 4 = 0
X = - 4
(b)
4x-3/2 + 7x+1/6 = 29/2
Since 6 is a least common multiple for all the denominators, we multiple all the fractions by 6;
((4x-3)/2)6 + ((7x+1)/6)6 = (29/2)6
3 (4x - 3) + (7x + 1) = 29 * 3
12x – 9 + 7x + 1 = 87
12x + 7x – 9 + 1 = 87
19x – 8 = 87
19x = 87 + 8
19x = 95
X = 5