Algebra help please answer fast?

Question

when solving an inequality, i know that when you divide or multiply a a negative number u reverse the sign (<, >)

but when solving something like this, how does it work?

-4<6x-10<14 the second < is supposed to have a underscore thing on the bottom, so can someone help me solve this. and also explain how the reverse works in these type of inequalitys?

thanks in advance.

Answer 1

-4 &lt; 6x - 10 ≤ 14

-4 + 10 &lt; 6x ≤ 14 + 10

6 &lt; 6x ≤ 24

6/6 &lt; x ≤ 24/6

1 &lt; x ≤ 4

Answer 2

you&#039;re not dividing by a neg number, so the signs would remain the same.  you want x alone in the middle so, whatever you do to one side of the inequality, you have to do to the other sides.

-4&lt;6x-10&lt;=14  add 10

6&lt;6x&lt;=24 divide by 6

1&lt;x&lt;=4  all done!

Answer 3

-4&lt;6x-10&lt;14

6&lt;6x&lt;24

1&lt;x&lt;4

x is greater than one and less than or equal to 4

Answer 4

in a compound inequality (like this one), the rule is still the same:

if you multiply or divide by a negative number, you reverse the direction of BOTH inequality symbols

for this particular inequality, you don&#039;t have to, but there are some where you do...

Answer 5

-4 &lt; 6x-10 &lt;_ 14

Add 10 to all 3 parts:

6 &lt; 6x &lt;_ 24

Divide by 6 at all 3 parts:

1 &lt; x &lt;_ 4

In the above case, we don&#039;t have to multiply or divide by a negative number. If we do, it works the same way as you&#039;ve described, just that we reverse all the inequality signs.

e.g. If we have...

6 &lt; -6x &lt; 24

Divide by -6 at all 3 parts.

-1 &gt; x &gt; -4

Since we don&#039;t usually do the signs like that, let&#039;s make it into a nicer format:

-4 &lt; x &lt; -1

Answer 6

-4&lt;6x-10&lt;14

-4+10&lt;6x-10+10&lt;10+14

6&lt;6x&lt;24

1&lt;x&lt;4

Answer 7

It can be read as

- 4 is less than 6x - 10 which is LESS THAN OR EQUAL TO (the underscore thing) 14.

Hope this answers your question.

Answer 8

-4 &lt; 6x -10 &lt;=14 here our aim is to find the value for that is the range  where the values of x lies . so we follow the steps.

-4+10&lt;6x-10+10&lt;=14+10

+6 &lt; 6X &lt;= 24 Since  6 is the factor divide by 6

1&lt; x  &lt; = 4  says thatx takes the values from 1 to 4

(ie) x={1,2,3,4}  

Answer 9

-4 &lt; 6x - 10 &lt;= 14

If you break this expression, it will be

- 4 &lt; 6x - 10  and 6x - 10 &lt;= 14

-4 + 10 &lt; 6x - 10 + 10

6 &lt;  6x

1 &lt; x

======

6x - 10 &lt;= 14

6x - 10 + 10 &lt;= 14 + 10

6x &lt;= 24

x &lt;=4

Your answer will be

1 &lt; x &lt;= 4

========

But you can also solve the expression simultaneously.

-4 &lt; 6x - 10 &lt;= 14

-4 + 10 &lt; 6x - 10 + 10 &lt;= 14 + 10

6 &lt; 6x &lt;= 24

1 &lt; x &lt;= 4

Don&#039;y worry about the inequality sign, treat them as = sign