Question

kuta software - infinite pre-algebra
name
date__________ period
simplifying variable expressions
simplify each expression.
*day 3 - assignment
show all work!

1. $-3p + 6p$
2. $b - 3 + 6 - 2b$
3. $7x - x$
4. $7p - 10p$
5. $-10v + 6v$
6. $-9r + 10r$
7. $9 + 5r - 9r$
8. $1 - 3v + 10$
9. $5n + 9n$
10. $4b + 6 - 4$
11. $35n - 1 + 46$
12. $-33v - 49v$
13. $30n + 8n$
14. $7x + 31x$
15. $10x + 36 - 38x - 47$
16. $-2(7 - n) + 4$
17. $-8(-5b + 7) + 5b$
18. $-4p - (1 - 6p)$
19. $4 - 5(-4n + 3)$
20. $-7(k - 8) + 2k$
21. $1 + 7(1 - 3b)$
22. $3 - 8(7 - 5n)$

Explanation:

Step1: Combine like terms

$-3p + 6p = (-3 + 6)p$

Step2: Calculate coefficient sum

$(-3 + 6)p = 3p$

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Step1: Combine like terms

$b - 2b + (-3 + 6) = (1 - 2)b + 3$

Step2: Calculate sums

$(1 - 2)b + 3 = -b + 3$

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Step1: Combine like terms

$7x - x = (7 - 1)x$

Step2: Calculate coefficient sum

$(7 - 1)x = 6x$

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Step1: Combine like terms

$7p - 10p = (7 - 10)p$

Step2: Calculate coefficient sum

$(7 - 10)p = -3p$

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Step1: Combine like terms

$-10v + 6v = (-10 + 6)v$

Step2: Calculate coefficient sum

$(-10 + 6)v = -4v$

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Step1: Combine like terms

$-9r + 10r = (-9 + 10)r$

Step2: Calculate coefficient sum

$(-9 + 10)r = r$

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Step1: Combine like terms

$9 + 5r - 9r = 9 + (5 - 9)r$

Step2: Calculate coefficient sum

$9 + (5 - 9)r = 9 - 4r$

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Step1: Combine constant terms

$1 + 10 - 3v = 11 - 3v$

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Step1: Combine like terms

$5n + 9n = (5 + 9)n$

Step2: Calculate coefficient sum

$(5 + 9)n = 14n$

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Step1: Combine constant terms

$4b + (6 - 4) = 4b + 2$

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Step1: Combine constant terms

$35n + (-1 + 46) = 35n + 45$

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Step1: Combine like terms

$-33v - 49v = (-33 - 49)v$

Step2: Calculate coefficient sum

$(-33 - 49)v = -82v$

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Step1: Combine like terms

$30n + 8n = (30 + 8)n$

Step2: Calculate coefficient sum

$(30 + 8)n = 38n$

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Step1: Combine like terms

$7x + 31x = (7 + 31)x$

Step2: Calculate coefficient sum

$(7 + 31)x = 38x$

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Step1: Group like terms

$10x - 38x + 36 - 47 = (10 - 38)x + (36 - 47)$

Step2: Calculate sums

$(10 - 38)x + (36 - 47) = -28x - 11$

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Step1: Distribute the multiplier

$-2(7 - n) + 4 = -14 + 2n + 4$

Step2: Combine constants

$-14 + 4 + 2n = 2n - 10$

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Step1: Distribute the multiplier

$-8(-5b + 7) + 5b = 40b - 56 + 5b$

Step2: Combine like terms

$40b + 5b - 56 = 45b - 56$

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Step1: Remove parentheses

$-4p - (1 - 6p) = -4p - 1 + 6p$

Step2: Combine like terms

$-4p + 6p - 1 = 2p - 1$

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Step1: Distribute the multiplier

$4 - 5(-4n + 3) = 4 + 20n - 15$

Step2: Combine constants

$20n + 4 - 15 = 20n - 11$

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Step1: Distribute the multiplier

$-7(k - 8) + 2k = -7k + 56 + 2k$

Step2: Combine like terms

$-7k + 2k + 56 = -5k + 56$

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Step1: Distribute the multiplier

$1 + 7(1 - 3b) = 1 + 7 - 21b$

Step2: Combine constants

$1 + 7 - 21b = 8 - 21b$

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Step1: Distribute the multiplier

$3 - 8(7 - 5n) = 3 - 56 + 40n$

Step2: Combine constants

$40n + 3 - 56 = 40n - 53$

Answer:

1. $3p$
2. $-b + 3$
3. $6x$
4. $-3p$
5. $-4v$
6. $r$
7. $9 - 4r$
8. $11 - 3v$
9. $14n$
10. $4b + 2$
11. $35n + 45$
12. $-82v$
13. $38n$
14. $38x$
15. $-28x - 11$
16. $2n - 10$
17. $45b - 56$
18. $2p - 1$
19. $20n - 11$
20. $-5k + 56$
21. $8 - 21b$
22. $40n - 53$