Integers Involving Variables 1
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Question 1 of 4
1. Question
Evaluate`6x-8x`- (-2x)
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Terms with the same variable can be added or subtracted.Both terms have `x` as their variable, meaning we can freely add or subtract them like integers.Since the signs are different `(+ -)` we will find the difference of the two numbers`8-6` `=` `2` Find the Difference `\text(Difference)` `=` `2` Insert the sign of the larger number `(-8)` to the difference as well as the variable `x`.`6x-8x` `=` `-2x` Insert a negative sign since the larger number, `8` is negative `-2x` -
Question 2 of 4
2. Question
Evaluate`4y-3x+y-7x`- (5y-10x, -10x+5y)
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Terms with the same variable can be added or subtracted.First, solve for the values with an `x` variable (`-3x-7x`).Since the signs are the same `(- -)` we will find the sum of the two numbers`3+7` `=` `10` Find the Sum `\text(Sum)` `=` `10` Insert the sign of the larger number `(-7)` to the difference as well as the variable `x`.`-3x-7x` `=` `-10x` Insert a negative sign since the larger number, `7` is negative Next, solve for the values with a `y` variable (`4y+y`).Since the signs are the same `(+ +)` we will find the sum of the two numbers`4+1` `=` `5` Find the Sum `\text(Sum)` `=` `5` Insert the sign of the larger number `(+4)` to the difference as well as the variable `y`.`4y+y` `=` `5y` Use a positive sign since the larger number, `5` is positive Finally, combine the terms.`5y-10x` `5y-10x` -
Question 3 of 4
3. Question
Evaluate`12+(-7x)+6x-(-18)`- (30-x, -x+30)
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Terms with the same variable can be added or subtracted.First, solve for the values with an `x` variable (`-7x+6x`).Since the signs are different `(- +)` we will find the difference of the two numbers`7-6` `=` `1` Find the Difference `\text(Difference)` `=` `1` Insert the sign of the larger number `(-7)` to the difference as well as the variable `x`.`-7x+6x` `=` `-x` Insert a negative sign since the larger number, `7` is negative Next, solve for the values with no variables.`12``-``(``-``18)` `=` `12``+``18` Recall, 
`=` `30` Finally, combine the terms.`30-x` `30-x` -
Question 4 of 4
4. Question
Evaluate`(-7m)^2divide-7m`- (-7m)
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Rules for Dividing Integers
Transform the expression into a fraction to make it easier to solve.`(-7m)^2divide-7m` `=` `((-7m)^2)/(-7m)` `=` `(49m^2)/(-7m)` Simplify the fraction$$\frac{\color{#00880A}{49}m^2}{\color{#CC0000}{-7}m}$$ `=` `-7``(m^2)/m` Recall, `=` `-7m^(2-1)` Recall rules for indices `=` `-7m^(1)` `=` `-7m` `-7m`
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