Simplify \(\frac{2x-1}{3}-\frac{x+3}{2}\)
\(\frac{x+3}{6}\)
\(\frac{x+8}{6}\)
\(\frac{x-11}{6}\)
\(\frac{x-4}{6}\)
Correct answer is C
\(\frac{2x - 1}{3} - \frac{x + 3}{2}\)
= \(\frac{2(2x - 1) - 3(x + 3)}{6}\)
= \(\frac{4x - 2 - 3x - 9}{6}\)
= \(\frac{x - 11}{6}\)
(6x - 5)(x + 4)
2(3x-5)(x+2)
(3x+4)(2x-5)
(3x-4)(2x+5)
Correct answer is D
\(6x^2 + 7x - 20\)
= \(6x^2 + 15x - 8x - 20\)
= \(3x(2x + 5) - 4(2x + 5)\)
= \((3x - 4)(2x + 5)\)
Evaluate \(\frac{x^2 + x - 2}{2x^2 + x -3}\) when x = -1
-2
-1
\(-\frac{1}{2}\)
1
Correct answer is D
\(\frac{x^2 + x - 2}{2x^2 + x - 3}\)
= \(\frac{x^2 + 2x - x - 2}{2x^2 + 3x - 2x - 3}\)
= \(\frac{x(x + 2) - 1(x + 2)}{x(2x + 3) - 1(2x + 3)}\)
= \(\frac{(x - 1)(x + 2)}{(x - 1)(2x + 3)}\)
= \(\frac{x + 2}{2x + 3}\)
At x = -1,
= \(\frac{-1 + 2}{2(-1) + 3}\)
= \(\frac{1}{1}\)
= 1
Given that y = px + q and y = 5 when x = 3, while y = 4 when x = 2, find the value of p and q.
p = 1, q = 3
p = 1, q = 2
p = -2, q = 3
p = 3, q = -2
Correct answer is B
y = px + q
5 = 3p + q ... (i)
4 = 2p + q ... (ii)
(i) - (ii) : p = 1
∴∴ 5 = 3(1) + q
⟹⟹ q = 5 - 3 = 2
(p, q) = (1, 2)
45 years
48 years
60 years
74 years
Correct answer is C
Let the sons age be x. The father is 4x ∴ 4x - x = 36; 3x = 36; x = 12 The son is 12 years and the father is 12 x 4 = 48. The sum of their ages (12 + 48) years = 60years