Illustrates that each of the following numbers are solutions to the following equation or inequality.
(a) x = 3 in x^{2} - 9 = 0
(b) y = 8 in 3( y + 1) = 4 y - 5
Solution
(a) First we plug the proposed solution in the equation.
9 - 9 = 0
0 = 0
Thus, what we are asking here is does the right side equivalent to the left side after we plug in the proposed solution. That is the meaning of the "?" above the equal sign in the first line.
As the right side & the left side are the similar we say that x = 3 satisfy the equation.
(b) Thus, we desire to see if y = 8 satisfies equation. First plug the value into the equation.
27=27
Thus, y = 8 satisfies the equation and thus is a solution.
We have also done a rapid example of numbers that aren't solution therefore we can see how these will work as well.