solve the inieqaulity

Question

3/X-2 + 4/X+5 < or = 0

again if you can only answer 1 problem that would be great. I really need help and i also need to know how you do the problem. THANKS IN ADVANCE

Answer 1

Given ineqality is 3/X - 2 + 4/X + 5 ≤ 0

3/x + 4/x - 2+ 5  ≤ 0   (Apply commutative property of addition a+b=b+a)

3/x + 4/x + 3 ≤ 0        (Add:-2+5=3)

7/x + 3 ≤ 0                 (Add:3/x+4/x=7/x)

7/x + 3-3 ≤ 0-3          (Subtract 3 from each side)

7/x + 0 ≤ -3               (Apply additive inverse property 3-3=0)

7/x × x ≤ -3x              (Multiply each side with x )

7 ≤ -3x                      (Cancel common terms)

7/3 ≤ -3x/3                (Divide each side by 3)

7/3 ≤ -x                     (Cancel common terms)

-(7/3) ≥ -(-x)             (Multiply each side with negative one and flip the symbol)

-7/3 ≥ x                          (Product of two same signs is positive)

x ≤ -7/3

The solution is x ≤ -7/3

Comments

Solution of the inequality is {x | x : -7/3 ≤ x < 0}.

Answer 2

The inequality is

• Step-1

State the exclude values,These are the values for which denominator is zero.

The exclude value of the inequality is 0.

• Step - 2

Solve the related equation.

7 + 3x  = 0

3x  = -7

x  = -7/3

Solution of related equation x  = -7/3

• Step-3

Draw the vertical lines at the exclude value and at the solution to separate the number line into intervals.

• Step-4

Now test  sample values in each interval to determine whether values in the interval satisify the inequality.

Test x  = -2.5

Above statement is false.

Test x  = -1

Above statement is true.

Test x  = 0.5

Above statement is false.

Test x  = -7/3

Above statement is true.

Test x = 0

Above statement is false.

The statement is true for x  = -1 and x  = -7/3.Therefore the solution is -7/3 ≤ x  < 0.

Solution {x | x : -7/3 ≤ x < 0}.