# Algebra - Substitution

*"Substitute" means to put in the place of another.*

## Substitution

In Algebra "Substitution" means putting numbers where the letters are:

When we have: | x − 2 | |

And we know that x=6 ... |
||

... then we can substitute 6 for x: |
6 − 2 = 4 |

### Example: When x=2, what is **10/x + 4** ?

Put "2" where "x" is:

10/2 + 4 = 5 + 4 = **9**

### Example: When x=5, what is **x + x/2** ?

Put "5" where "x" is:

5 + 5/2 = 5 + 2.5 = **7.5**

### Example: If x=3 and y=4, then what is **x**^{2} + xy ?

^{2}+ xy

Put "3" where "x" is, and "4" where "y" is:

3^{2} + 3×4 = 3×3 + 12 = **21**

### Example: If x=3 (but we don't know "y"), then what is **x**^{2} + xy ?

^{2}+ xy

Put "3" where "x" is:

3^{2} + 3y = **9 + 3y**

(that is as far as we can get)

As that last example showed, we may not always get a number for an answer, sometimes just a simpler formula.

## Negative Numbers

When we substitute negative numbers, it is best to put () around them so we get the calculations right.

### Example: If x = **−2**, then what is **1 − x + x**^{2} ?

^{2}

Put "(−2)" where "x" is:

**1 −** **(−2)**** +** **(−2)**** ^{2}** = 1 + 2 + 4 = 7

In that last example:

- the
**− (−2)**became**+2** - the
**(−2)**became^{2}**+4**

because of these special rules:

Rule | Adding or Subtracting |
Multiplying or Dividing |
||
---|---|---|---|---|

Two like signs become a positive sign |
3+(+2) = 3 + 2 = 5 |
3 × 2 = 6 | ||

6−(−3) = 6 + 3 = 9 |
(−3) × (−2) = 6 | |||

Two unlike signs become a negative sign |
7+(−2) = 7 − 2 = 5 |
3 × (−2) = −6 | ||

8−(+2) = 8 − 2 = 6 |
(−3) × 2 = −6 |

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