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Equations without equals to sign

These questions are from millions of online tutorials and YouTube websites. I don’t know if I am allowed to ask experts to explain those questions in a different way. They are not homework assignments. I am trying to develop my own web site. Math’s has many ways to solve the problems. Just want to understand them.

1. How to solve these kind of questions when there is no equals to sign in it?
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mustish1
Asked:
mustish1
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1 Solution
 
Paul SauvéCommented:
the < and > sign replace the = signs in this type of equation.

these can be treated as a regular equation, but you must keep the greater than (>) or the less than (<) signs in the initial order

- 4x - 9 > 7

(- 4x - 9) + 9 > (7) + 9     comment: intermediate equation―adding + 9 to both sides of the inequality does not change it

- 4x > 16

(- 4x) / -4 > (16)  / -4      comment: intermediate equation―dividing both sides of the inequality by -4 does not change it

the final answer is:
x > -4

Also, on the graphs, by CONVENTION:

the square brackets [ or ] include the number
the round brackets ( or ) exclude the number
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n2fcCommented:
This is an example of an "INEQUALITY" equation...

By using a "less than" "greater than" (or combined with equals) they represent a RANGE of answers, not a single discrete value as in an EQUALITY equation...

Basically use the same rules to solve as in a regular algebraic equation (i.e.  perform same operation to both sides to keep it balanced)...
NOTE***
The Exception: Negative Numbers. There is one very important exception to the rule that multiplying or dividing an inequality is the same as multiplying or dividing an equation. Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.

SO... STEP BY STEP:

-4x -9 > 7
*** ADD 9 to each side

-4x > 16
***  DIVIDE each side by 4

-x  > 4
*** THIS STEP IS UNIQUE to INEQUALITIES!   REVERSE SIGNS OF EACH SIDE, AND REVERSE INEQUALITY!

x < -4

The selected graph (b) shows the correct RANGE of values, i.e. all numbers LESS THAN (but not including) -4!

Make sense?
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mustish1Author Commented:
Thank You.
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Paul SauvéCommented:
>> *** THIS STEP IS UNIQUE to INEQUALITIES!   REVERSE SIGNS OF EACH SIDE, AND REVERSE INEQUALITY!

yep - MY bad... I has been a LONG time since I studied ALGEBRA (in the 1960's)
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n2fcCommented:
Interesting... Paul gets the "accepted" with the WRONG answer!

Oh, well...
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mustish1Author Commented:
I think its a typo mistake. Rest of the steps are correct.
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Paul SauvéCommented:
the points were split evenly - does it really matter?
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n2fcCommented:
Not really...   Just a minor concern over someone doing a search in the future and not fully reading the entire thread!

Enjoy!
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Paul SauvéCommented:
just saying - this happens all the time

i've posted correct answers and someone subsequently posting the same answer gets the points & i get none

no offense meant or taken :-)
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