if \(\frac{4m+3n}{4m-3n}=\frac{5}{2}\), find the ratio m:n
7:4
4:3
3:4
4:7
Correct answer is A
\(\frac{4m + 3n}{4m - 3n} = \frac{5}{2}\)
\(5(4m - 3n) = 2(4m + 3n)\)
\(20m - 15n = 8m + 6n\)
\(20m - 8m = 6n + 15n\)
\(12m = 21n\)
\(\frac{21}{12} = \frac{m}{n}\)
\(m : n = 7 : 4\)
If \(\frac{y-3}{2}<\frac{2y-1}{3}\), which of the following is true?
y > 7
y < -7
y > -7
y < 7
Correct answer is C
\(\frac{y - 3}{2} < \frac{2y - 1}{3}\)
\(3(y - 3) < 2(2y - 1)\)
\(3y - 9 < 4y - 2\)
\(3y - 4y < -2 + 9\)
\(-y < 7\)
\(y > -7\)
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