Evaluate the inequality \(\frac{x}{2} + \frac{3}{4} \leq \frac{5x}{6} - \frac{7}{12}\)
\(x \geq 4\)
\(x \leq 3\)
\(x \geq -3\)
\(x \leq -4\)
Correct answer is A
\(\frac{x}{2} + \frac{3}{4} \leq \frac{5x}{6} - \frac{7}{12}\)
\(12\frac{x}{2} + 12\frac{3}{4} \leq 12\frac{5x}{6} - 12\frac{7}{12}\)
6x + 9 \(\leq\) 10x - 7
6x - 10x \(\leq\) - 7 - 9
-4x \(\leq\) -16
-4x/-4 \(\geq\) -16/-4
x \(\geq\) 4
What is the solution of \(\frac{x - 5}{x + 3} < -1\)?
-3 < x < 1
x < -3 or x > 1
-3 < x < 5
x < -3 or x > 5
Correct answer is A
Consider the range -3 < x < -1
= { -2, -1, 0}, for instance
When x = -2,
\(\frac{-2 - 5}{-2 + 3} < -1\)
\(\frac{-7}{1} < -1\)
When x = -1,
\(\frac{-1 - 5}{-1 + 3} < -1\)
\(\frac{-6}{2} < -1\)
= -3 < -1
When x = 0,
\(\frac{0 - 5}{0 + 3} < -1\)
\(\frac{- 5}{3} < -1\)
Hence -3 < x < 1
(2y - 3x) (y + 6x)
(2y - 3x) (y - 6x)
(2y + 3x) (y - 6x)
(3y + 2x) (y - 6x)
Correct answer is B
2y2 - 15xy + 18x2
2y2 - 12xy - 3xy + 18x2
2y(y - 6x) - 3x(y - 6x)
(2y - 3x) (y - 6x)
If gt2 - k - w = 0, make g the subject of the formula
\(\frac{k + w}{t^2}\)
\(\frac{k - w}{t^2}\)
\(\frac{k + w}{t}\)
\(\frac{k - w}{t}\)
Correct answer is A
gt2 - k - w = 0
gt2 = k + w
\(g = \frac{k + w}{t^2}\)
If P = {1,2,3,4,5} and P \(\cup\) Q = {1,2,3,4,5,6,7}, list the elements in Q
{6}
{7}
{6,7}
{5,6}
Correct answer is C
Q = (P \(\cup\) Q) - P
{6,7}