a)
True or false?
b)
True or false?
Can you please help me understand this.
Here's B anyway since it's more involved....
Square both sides...
Subtract 36, 7x, and 2 from the right.
Look, we can divide the equation by -6.
Square both sides again...
Distribute the 4.
Subtract 28x and 8 from the right.
This factors to...
So our solutions are 14 and 2. Check them! You will find that 2 is the only solution and thus the statement is true.
Were those really "true or false" questions? I would interpret "true or false" for an equation involving, say, x, to be asking if it was true for all x- and that's clearly false for both questions.
To solve equations involving , you square to get rid of the square roots. After getting to , square again to get which is the same as . Either x= 0 or x- 4= 0 so x= 4.
Since squaring both sides like that can introduce "extraneous roots", you should always check by putting the numbers into the original equation. The original equation was [tex]\sqrt{2x+1}- \sqrt{x}= 1[tex]. With x= 0 that becomes so x= 0 is a solution. With x= 4, it becomes so x= 4 is also a solution.