Integers Involving Variables 2
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Question 1 of 4
1. Question
Evaluate`-8a-5a`- (-13a)
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Terms with the same variable can be added or subtracted.Both terms have `a` as their variable, meaning we can freely add or subtract them like integers.Since the signs are the same `(- -)` we will find the sum of the two numbers`8+5` `=` `13` Find the Sum `\text(Sum)` `=` `13` Insert the sign of the larger number `(-8)` to the difference as well as the variable `a`.`-8a-5a` `=` `-13a` Insert a negative sign since the larger number, `8` is negative `-13a` -
Question 2 of 4
2. Question
Evaluate`9x-(-3x)-16-(-7x)+24`- (19x+8, 8+19x)
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Terms with the same variable can be added or subtracted.First, solve for the values with an `x` variable.`9x``-``(``-``3x)``-``(``-``7x)` `=` `9x``+``3x``+``7x` Recall, 
`=` `19x` Next, solve for the values with no variables.Since the signs are the same `(- +)` we will find the difference of the two numbers`24-16` `=` `8` Find the Difference `\text(Difference)` `=` `8` Insert the sign of the larger number `(+24)` to the difference.`-16+24` `=` `8` Use a positive sign since the larger number, `24` is positive Finally, combine the terms.`19x+8` `19x+8` -
Question 3 of 4
3. Question
Evaluate`7x-(-x)-12-(+15x)+30`- (-7x+18, 18-7x)
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Terms with the same variable can be added or subtracted.First, solve for the values with an `x` variable.`7x``-``(``-``x)-(+15x)` `=` `7x``+``x-(+15x)` Recall, `7x+x``-``(``+``15x)` `=` `7x+x``-``15x` Recall, 
`=` `8x-15x` Since the signs are different `(+ -)` we will find the difference of the two numbers`15-8` `=` `7` Find the Difference `\text(Difference)` `=` `7` Insert the sign of the larger number `(-15)` to the difference as well as the variable `x`.`8x-15x` `=` `-7x` Insert a negative sign since the larger number, `15` is negative Next, solve for the values with no variables.Since the signs are different `(- +)` we will find the difference of the two numbers`30-12` `=` `18` Find the Difference `\text(Difference)` `=` `18` Insert the sign of the larger number `(+30)` to the difference.`-12+30` `=` `18` Use a positive sign since the larger number, `30` is positive Finally, combine the terms.`-7x+18` `-7x+18` -
Question 4 of 4
4. Question
Evaluate`-32y^3divide-8y`Hint
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Rules for Dividing Integers
Transform the expression into a fraction to make it easier to solve.`-32y^3divide-8y` `=` `(-32y^3)/(-8y)` Simplify the fraction$$\frac{\color{#CC0000}{-32}y^3}{\color{#CC0000}{-8}y}$$ `=` `4``(y^3)/y` Recall, `=` `4y^(3-1)` Recall rules for indices `=` `4y^(2)` `=` `4y^2` `4y^2`
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