Question

1.) -8 2.) 3 3.) 9 4.) -19 5.) -1 6.) -17
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adding like variable terms
reminder: when there is a number written next to a variable, that number is called the coefficient. in the term -3x, the number -3 is the coefficient of x.
you should remember from pre - algebra #2 that we can only add and subtract like terms. those are terms that have the same variables but possibly different coefficients.
example 1: 2x + 3x = 5x we may add 2x and 3x because they are both terms with the variable x. we add the 2 + 3 to get a total of 5x.
review practice adding like terms with positive coefficients:
1.) 6x + 4x =
2.) 3x + 6x =
3.) 9x + 8x =
4.) 7x + 5x =

variables with unlike signs
now that you have studied and reviewed integers, you can work the following example:
example 2: -2x + 3x = 1x or x
\1x\ can be written without the coefficient \1.\
we obtain the result above by combining the coefficients: -2x + 3x = 1x because -2 + 3 = 1.
example 3: 4x + (-7x) = -3x because 4 + (-7) = -3.
practice: add like terms to simplify using the rules for integers with unlike signs.
1.) -5y + 9y =
2.) -9b + 7b =
3.) -6b + 8b =
4.) -4t + 2t =
5.) -2ab + 7ab =
6.) -3a + a =
remember “a” = “1a.”
7.) -8xy + 4xy =
8.) -5z + 18z =
9.) 7x + (-10x) =
10.) 5x + (-3x) =

Explanation:

Step1: Solve \(6x + 4x\)

Add the coefficients of \(x\) (6 and 4) since they are like terms. \(6 + 4 = 10\), so \(6x + 4x = 10x\).

Step2: Solve \(3x + 6x\)

Add the coefficients 3 and 6. \(3 + 6 = 9\), so \(3x + 6x = 9x\).

Step3: Solve \(9x + 8x\)

Add coefficients 9 and 8. \(9 + 8 = 17\), so \(9x + 8x = 17x\).

Step4: Solve \(7x + 5x\)

Add coefficients 7 and 5. \(7 + 5 = 12\), so \(7x + 5x = 12x\).

Step5: Solve \(-5y + 9y\)

Add coefficients -5 and 9. \(-5 + 9 = 4\), so \(-5y + 9y = 4y\).

Step6: Solve \(-9b + 7b\)

Add coefficients -9 and 7. \(-9 + 7 = -2\), so \(-9b + 7b = -2b\).

Step7: Solve \(-6b + 8b\)

Add coefficients -6 and 8. \(-6 + 8 = 2\), so \(-6b + 8b = 2b\).

Step8: Solve \(-4t + 2t\)

Add coefficients -4 and 2. \(-4 + 2 = -2\), so \(-4t + 2t = -2t\).

Step9: Solve \(-2ab + 7ab\)

Add coefficients -2 and 7. \(-2 + 7 = 5\), so \(-2ab + 7ab = 5ab\).

Step10: Solve \(-3a + a\)

Rewrite \(a\) as \(1a\), then add coefficients -3 and 1. \(-3 + 1 = -2\), so \(-3a + a = -2a\).

Step11: Solve \(-8xy + 4xy\)

Add coefficients -8 and 4. \(-8 + 4 = -4\), so \(-8xy + 4xy = -4xy\).

Step12: Solve \(-5z + 18z\)

Add coefficients -5 and 18. \(-5 + 18 = 13\), so \(-5z + 18z = 13z\).

Step13: Solve \(7x + (-10x)\)

Add coefficients 7 and -10. \(7 + (-10) = -3\), so \(7x + (-10x) = -3x\).

Step14: Solve \(5x + (-3x)\)

Add coefficients 5 and -3. \(5 + (-3) = 2\), so \(5x + (-3x) = 2x\).

Answer:

1. \(10x\)
2. \(9x\)
3. \(17x\)
4. \(12x\)
5. \(4y\)
6. \(-2b\)
7. \(2b\)
8. \(-2t\)
9. \(5ab\)
10. \(-2a\)
11. \(-4xy\)
12. \(13z\)
13. \(-3x\)
14. \(2x\)