If |x+2| \(\le\) 9, then x belongs to

(a)

\((-\infty ,-7)\)

(b)

[-11, 7]

(c)

\((-\infty ,-7)\cup (11,\infty)\)

(d)

(-11, 7)

Given that x, y and b are real numbers x < y, b > 0, then

(a)

xb < yb

(b)

xb > yb

(c)

xb ≤ yb

(d)

\(\frac { x }{ b } \ge \frac { y }{ b } \)

If \(\frac { |x-2| }{ x-2 } \ge 0\), then x belongs to

(a)

\([2,\infty]\)

(b)

\((2,\infty )\)

(c)

\((-\infty,2)\)

(d)

\((-2,\infty )\)

The solution 5x-1<24 and 5x+1 > -24 is

(a)

(4,5)

(b)

(-5,-4)

(c)

(-5,5)

(d)

(-5,4)

The solution set of the following inequality |x-1| \(\ge\) |x-3| is

(a)

[0, 2]

(b)

\([2,\infty)\)

(c)

(0, 2)

(d)

\((-\infty,2)\)

If x < 7, then ___________

(a)

-x < -7

(b)

- x ≤ -7

(c)

-x > -7

(d)

-x ≥ -7

If - 3x + 17 < -13 then ___________

(a)

x ∈ (10, ∞)

(b)

x ∈ [10, ∞)

(c)

x ∈ (-∞, 10]

(d)

x ∈ [10, 10)

If |x + 3| ≥ 10 then ___________

(a)

x ∊ (-13, 7]

(b)

x ∊ [-13, 7)

(c)

x ∊ (-∞, -13] \(\cup\) [7, ∞)

(d)

x ∊ (-∞, -13] \(\cup\) [7, ∞)

\(\sqrt [ 4 ]{ 11 } \) is equal to ___________

(a)

\(\sqrt [ 8 ]{ 11^{ 2 } } \)

(b)

\(\sqrt [ 8 ]{ 11^{ 4 } } \)

(c)

\(\sqrt [ 8 ]{ 11^{ 8 } } \)

(d)

\(\sqrt [ 8 ]{ 11^{ 6 } } \)

Simplify \(\left( 125 \right) ^{ \frac { 2 }{ 3 } }\)

Simplify \({ 16 }^{ -\frac { 3 }{ 4 } }\)

Simplify \((-1000)^{ \frac { -2 }{ 3 } }\)

Simplify \(\left( 3^{ -6 } \right) ^{ \frac { 1 }{ 3 } }\)

Simplify \(\frac { { (27) }^{ \frac { -2 }{ 3 } } }{ { (27) }^{ \frac { -1 }{ 3 } } } \)

Solve the inequation 5x - 1 < 15 when x is a natural number

If k > 0, then solve the inequation |x| ≤ K

A solution is to be kept between 68^oF and 77^oF. What is the range in temperature in degree Celsius (c) or Fahrenheit (F), conversion formula is given by \(F=\frac { 9 }{ 5 } \)C + 32?

Solve the linear in equation 4 - x \(\le\) 3x + 12.

Solve the quadratic equation 5^2x- 5^{x + 3}+ 125 = 5^x.

Simplify \(\frac { 1 }{ 3-\sqrt { 8 } } -\frac { 1 }{ \sqrt { 8 } -\sqrt { 7 } } +\frac { 1 }{ \sqrt { 7 } -\sqrt { 6 } } -\frac { 1 }{ \sqrt { 6 } -\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } -2 } \)

Solve \(\frac { 1 }{ \left| 2x-1 \right| } <6\) and express the solution using the interval notation.

Solve \(\sqrt [ 8 ]{{{x}\over{x+3}} } -\sqrt{{{x+3}\over{x}}}=2.\)

Prove that \(\sqrt { 3 } \) is an irrational number. (Hint: Follow the method that we have used to prove \(\sqrt { 2 } \notin Q\))

Solve : \({{2x+5}\over{x-1}}>5\)