-x > -4, -2x < -1 , 5/6x >4/5 Does somebody help me with?>?

Question

please help to solve them i have more but i just need one of each of them.

Answer 1

-x&gt;-4 / multiply with -1 (when you multiply with negative, you change &quot;sign&quot;)

x&lt;4

-2x&lt;-1 / multiply with -1 again

2x&gt;1

x&gt;1/2

5/6 x&gt;4/5

x&gt;4/5 / 5/6

x&gt;4/5 * 6/5

x&gt;24/25

good luck!

Answer 2

-x &gt; -4

divide both sides by -4 and you get

x &lt; 4

(sign switches, yes)

-2x &lt; -1

divide both sides by -2 and you get

x &gt; 1/2

5/6x &gt; 4/5

divide both sides by 5/6 and you get

x &gt; 24/25

Hope I helped!!

Answer 3

The value x = 1 satisfies all the three equations.

Answer 4

You have three equations:

(1) -x &gt; -4      

Multiply both sides of the equation by (-1) which forces you to reverse the direction of the inequality sign.

x &lt; 4

(2) -2x &lt; -1

Again, multiply both sides of the equation by (-1) which forces you to reverse the direction of the inequality sign.

2x &gt; 1

x &gt; 1/2

(3) 5x/6 &gt; 4/5

The least common denominator of these two fractions is 5 * 6 = 30.

I am using * for the multiplication symbol.  Multiply both sides of the equation by 30.

[((30 * 5) * x ]/ 6) &gt; ((30 * 4) / 5)

(150x) / 6 &gt; 120 / 5

25x &gt; 24

We now that that

(1) x &lt; 4

(2) x &gt; 1/2          and

(3) x &gt; 24/25

Thus:    1/2 &lt; x &lt; 4 is the final answer.   &lt;&lt;&lt;&lt;&lt;

You have infinitely many numbers between 1/2 and 4 to choose from.

The x &gt; 24/25 gave us no additional information.