Inequalities
Comments: 1
True, False, and Open Sentences
There are three ways to identify equations: true, false, or open.
5+3=8 is a true equation because we know that it is true -- 5+3 does equal eight.
5+3=7 is a false equation because 5+3 does not equal seven, it equals eight.
x+3=8 is an open equation because we do not know what x is, so the equation depends on what x is.
To find out what x is, we use the same system used when finding what x equals in other algebraic equations:
X + 3 = 8
↓ - 3 ↓ - 3
X = 5
- Subtract three from where you added three.
- Subtract three from eight to balance the equation.
- Bring down the X and the = sign.
Inequality equations look very similar. However, they do not have an "equals" sign. Instead, they have "greater than" and "less than" symbols: 3+5<9 is true. 3+5>9 is false. X+5>9 is open, because it depends on what x is. To find what x is, you use the same system as the one used above to find the answer to an algebraic expression:
X + 5 > 9
↓ - 5 ↓- 5
X > 5
We can change the > sign to the > sign, which is a combination of the two signs = and >, which means that the variable and number (x and 5) can be either greater than or equal to the nine.
On a number line, this is how an inequality equation would look:
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This is an excellent introduction to true, false, and open sentences. Your entry looks great too--the solving of the equations is easy to follow. I would have liked to have seen a little more explanation of the solution to the inequality: what does x > 5 mean? What does the graph show?
Mr. Tubbs
