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Consider the equation (x – 9)2 = x – 7. Is x = 11 a solution to this equation?
First evaluate the left-hand side expression for x = 11:
(11 – 9)2 = (2)2 = 4
Then evaluate the right-hand side expression for x = 11:
11 – 7 = 4
Because the left-hand and right-hand expressions match for x = 11, 11 is a solution to the equation. We can hang onto this one; we don't need to recycle it. Which is a shame, because we could've gotten 10 cents for it down at the grocery store.
Is y = 3 a solution to the equation y + 2 = 2y?
First evaluate the left-hand side expression for y = 3:
3 + 2 = 5
Then evaluate the right-hand side expression for y = 3:
2(3) = 6
Since 5 definitely isn't equal to 6, the left- and right-hand sides of this equation don't give us to the same number when y = 3. So nope, y = 3 is not a solution to the equation y + 2 = 2y. Adios, y = 3. Go peddle your falsehood to some other sucker.
Be Careful: Work with the left and right sides of the equation separately. Otherwise, you'll be in danger of writing false equations or making a wrong turn. You don't want to make a wrong turn, because then it'll take your GPS like a minute and a half to recalculate.
Is x = 2 a solution to the equation x2 = 3x?
If we write down (2)2 = 3(2), we're lying. Sorry. We'll never do it again.
Let's figure out, without lying, if x = 2 is a solution to the equation.
First evaluate the left-hand side expression for x = 2:
(2)2 = 4
Then evaluate the right-hand side expression for x = 2:
3(2) = 6
Because 4 doesn't equal 6, x = 2 is not a solution to the equation x2 = 3x. Ah. It feels oh-so-much better to arrive at the answer honestly, doesn't it?