Integers Involving Variables 3
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Question 1 of 4
1. Question
Evaluate`4a-2b-6a+8b`- (-2a+6b, 6b-2a)
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Terms with the same variable can be added or subtracted.First, solve for the values with an `a` variable (`4a-6a`).Since the signs are different `(+ -)` we will find the difference of the two numbers`6-4` `=` `2` Find the Difference `\text(Difference)` `=` `2` Insert the sign of the larger number `(-6)` to the difference as well as the variable `a`.`4a-6a` `=` `-2a` Insert a negative sign since the larger number, `6` is negative Next, solve for the values with a `b` variable (`-2b+8b`).Since the signs are different `(- +)` we will find the difference of the two numbers`8-2` `=` `6` Find the Difference `\text(Difference)` `=` `6` Insert the sign of the larger number `(+8)` to the difference as well as the variable `b`.`-2b+8b` `=` `6b` Use a positive sign since the larger number, `8` is positive Finally, combine the terms.`-2a+6b` `-2a+6b` -
Question 2 of 4
2. Question
Evaluate`-24a^2divide-6a`- (4a)
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Rules for Dividing Integers
Transform the expression into a fraction to make it easier to solve.`-24a^2divide-6a` `=` `(-24a^2)/(-6a)` Simplify the fraction$$\frac{\color{#CC0000}{-24}a^2}{\color{#CC0000}{-6}a}$$ `=` `4``(a^2)/a` Recall, `=` `4a^(2-1)` Recall rules for indices `=` `4a^(1)` `=` `4a` `4a` -
Question 3 of 4
3. Question
Evaluate`m+3n-18m-4n+5`- (-17m-n+5)
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Terms with the same variable can be added or subtracted.First, solve for the values with an `m` variable (`m-18m`).Since the signs are different `(+ -)` we will find the difference of the two numbers`18-1` `=` `17` Find the Difference `\text(Difference)` `=` `17` Insert the sign of the larger number `(-18)` to the difference as well as the variable `m`.`m-18m` `=` `-17m` Insert a negative sign since the larger number, `18` is negative Next, solve for the values with a `n` variable (`3n-4n`).Since the signs are different `(+ -)` we will find the difference of the two numbers`4-3` `=` `1` Find the Difference `\text(Difference)` `=` `1` Insert the sign of the larger number `(-4)` to the difference as well as the variable `n`.`3n-4n` `=` `-n` Insert a negative sign since the larger number, `4` is negative Finally, combine the terms.Don’t forget to add the constant, `5`.`-17m-n+5` `-17m-n+5` -
Question 4 of 4
4. Question
Evaluate`8axx(-3b)xx2`- (-48ab)
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Rules for Multiplying Integers
First, separate the variables from the coefficients to make the solution easier.`8xx(-3)xx2xxaxxb` Next, perform the multiplication.`8xx(-3)``xx2xxaxxb` `-24``xx2xxaxxb` Recall, `-24xx2``xxaxxb` `-48``xxaxxb` Recall, `-48ab` Add the variables back to the coefficient `-48ab`
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