# interval notation

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1) Solve the following inequality. Write the answer in interval notation. X/X+3 ≤ -2/5(X-3)

2) Solve the inequality. 3 < |5X+3| < 5

3) a)Find an equation of the line, say y=mx+b, which passes through the point (-3,8) and is perpendicular to the line 3x+3y=33. y=?

b)What is the shortest distance from the point (-3,8) to the line 3x+3y=33? Shortest distance=?

4) Answer the following, assuming that all angels are in radian.

a) Suppose that X=6π /19 is a solution of the equation sin X= A, where A is some constant. Then A must be equal to ________, and the other solution of the equation in the interval [0,2π ] must be X=_______.

b)Suppose that X=π /13 is a solution of the equation cos X= B, where B is some constant. Then B must be equal to _______, and the other solution of the equation in the interval [0,2π ] must be X=_______.

c)Suppose that X=4π /7 is a solution of the equation tan X= C, where C is some constant. Then C must be equal to _______, and the other solution of the equation in the interval [0,2π ] must be X=__________.

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The solution provides answers to questions regarding interval notation.

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1) Solve the following inequality. Write the answer in interval notation.

X/X+3 ≤ -2/5(X-3)

Now check the sign of inequality in the intervals (-∞, -3), (-3, 3/5], [3/5, 2], [2, 3) and (3, ∞).

Take x = -4 from the interval (-∞, -3)

> 0

Take x = 0 from the interval (-3, 3/5]

< 0

Take x = 1 from the interval [3/5, 2]

> 0

Take X = 2.5 from the interval [2, 3)

< 0

Take x = 4 from the interval (3, ∞)

> 0

Thus, the solution is (-3, 3/5] or [2, 3)

Answer: (-3, 3/5] or [2, 3)

2) Solve the inequality. 3 < |5X+3| < 5

Solution:

We can divide it into two inequalities.

3 < |5X + 3| or |5X+3| < 5

That is

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