In this lesson, we will look at how to use the distributive property to simplify subtraction problems such as $7-({^-2x} + 3)$
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Do you think you have it? Try these 3 examples.
1. $4x-(3x+7)$
2. $x+6-7(2x-3)$
3. $x-(x+2)$
Review of how to use the distributive property and subtraction:
To distribute the negative in the expression $-(x+{^-2})$ you would take the opposite of everything in the parentheses (remember: the opposite of a number is the same as multiplying the number by $-1$.)
| $-(x+{^-2})$ |
| $-1x+({^-1}*{^-2})$ |
| $-x+2$ |
| If you had a problem like: | $7-2x(3+y)$ |
| you would change the subtraction problem to an addition problem by adding the opposite: | $7+{^-2x}(3+y)$ |
| Multiply each term by -2x: | $7+{^-2x}*3+{^-2x}*y$ |
| Simplify: | $7+{^-6x}+{^-2xy}$ |
Try these problems:
1. $-(2x-y)$
2. $7x-5y-(3x+5y)$
3. $5x+4n-3(2x-5n)$
Answer:
| 1a. Original problem:. | $-(2x-y)$ |
| b. Distribute the negative to each of the terms in the parenthesis. | ${^-2}$ $-$ ${^-y}$ |
| c. Change the subtraction to adding the opposite | ${^-2x}+y$ |
| ………………………………………….. | ……………………………. |
| 2a. Original problem: | $7x-5y$ $-$ $(3x+5y)$ |
| b. Distribute the negative to each of the terms in the parenthesis. | $7x-5y$ $+$ ${^-3x}+{^-5y}$ |
| c. Combing like terms | $7x$ $-$ $5y$ $+{^-3x}$ $+{^-5y}$ |
| d. Solution: | $4x-10y$ |
| ………………………………………….. | ……………………………. |
| 3a. Original problem: | $5x+4n$ $-$ $3$$(2x-5n)$ |
| b. Change the subtraction to adding the opposite | $5x+4n$ $+$ ${^-3}$$(2x-5n)$ |
| c. Distribute the ${^-3}$ to each of the terms in the parenthesis. | $5x+4n$ $+$ ${^-3}*2x-{^-3}*5n$ |
| d. Combine like terms | $5x$ $+$ $4n$ $+$ ${^-6x}$ $+$ ${15n}$ |
| e. Solution: | $-x+19n$ |
