It would be positive 1/3 because if you move to the right one on your bottom point and up 3 it gives you +1/3
28/81 is less than 7/9
28/81 is less than 4/9
The common denominator is 81, so you say 9 can go into 81 nine times, so you multiply 9 by the numerator, so 7/9 is now 63/81 an 4/9 is now 36/81
Complete the square to rewrite the quadratic:
2 <em>x</em>² + 3 <em>x</em> + 5 = 2 (<em>x</em>² + 3/2 <em>x</em>) + 5
... = 2 (<em>x</em>² + 3/2 <em>x</em> + 9/16 - 9/16) + 5
... = 2 (<em>x</em>² + 3/2 <em>x</em> + (3/4)²) + 5 - 9/8
... = 2 (<em>x</em> + 3/4)² + 31/8
Any real number squared becomes non-negative, so the quadratic expression has a minimum value of 31/8, which is greater than 0, and so there are no (real) <em>x</em> for which <em>y</em> = 0.
Linear equations are all solved the same way. Figure out the operations performed on the variable. Undo those in reverse order.
Here, the variable is
- divided by 2
- has -7 added.
In reverse order, we undo these operations by
- adding 7
- multiplying by 2.
Whatever we do to one side of an equation, we must also do to the other side. That is how the equal sign remains valid.
2 = m/2 -7
2 +7 = m/2 -7 +7 . . . . . add 7
9 = m/2 . . . . . . . . . . . . simplify
2*9 = 2*m/2 . . . . . . . . multiply by 2
18 = m . . . . . . . . . . . . . simplify. (You know that 2/2 = 1, and m*1 = m.)
The answer is m = 18.
_____
Check:
.. 2 = 18/2 -7
.. 2 = 9 -7 . . . . . . . true. The answer checks OK.
