solve this inequalities -1/2x-2>8

Question

Inequalities

Answer 1

Given inequality -1/2x-2>8

add 2 to each side.

-1/2x-2+2 > 8+2

-1/2x > 10

Multiple to each side by negitive two and change the symbol.

-2(-1/2)x > 10*-2

x < -20

Solution x < -20

x < -20

 

Answer 2

• Step - 1

Write the inequality in general form with the rational expression on the left and zero on the right.

The inequality is

Multiply each side by negitive one and flip the symbol of inequality.

The above rational inequality numarator critical value at x = 15/16

The above rational inequality denominator critical value at x = 1

• Step-2

Our critical points make partition the x - axis into 3 intervals.

Pick a point on each interval.

x  = 0.8, x  = 0.95 and x  = 1.1

Now compute 

The rational inequality

f (0.8) > 0 f(x) will be positive on (∞,15/16),Since f(0.95) < 0 f(x) will be negitive in interval (15/16,1),Since f (1.1) > 0 f (x ) will be positive on (1,∞)

We indicate this on the x - axis by inserting plus or minus signs on the x - axis. I use color coding instead: green for positive, red for negative:

Observe the graph ,The open circle meansthat 15/16 and 1 does not solutions of the inequality.

So we are looking for all x such that f (x ) < 0,Consequently the set (15/16, 1)

Solution of the inequality is 15/16 < x < 1

Solution.