simplifying linear expressions
simplify each expression.
1) 10x - 8x + 2 + 10
2) 3a + 7 + 2(3 + a)
3) 3(m - 5) + m
4) 2s + 10 - 7s - 8 + 3s - 7
5) 8c - 4 - 2c + 5
6) -4 + 7z + 3 - 2z
7) 15 + 4(5y - 10)
8) 2d + 17 - 3 - 2d + 4d
9) 12n - 8 - 2n + 10 - 4
10) 8(2k + 1 + 3k)
11) 4(2b + 2) - 3
12) -4 + 8p - 6p - 5 + 20p

Question

Accepted Answer

### Problem 1: $10x - 8x + 2 + 10$
# Explanation:
## Step1: Combine like terms for $x$
$10x - 8x = (10 - 8)x = 2x$
## Step2: Combine constant terms
$2 + 10 = 12$
## Step3: Combine results
$2x + 12$
# Answer: $2x + 12$

### Problem 2: $3a + 7 + 2(3 + a)$
# Explanation:
## Step1: Distribute the 2
$2(3 + a) = 6 + 2a$
## Step2: Combine like terms for $a$
$3a + 2a = 5a$
## Step3: Combine constant terms
$7 + 6 = 13$
## Step4: Combine results
$5a + 13$
# Answer: $5a + 13$

### Problem 3: $3(m - 5) + m$
# Explanation:
## Step1: Distribute the 3
$3(m - 5) = 3m - 15$
## Step2: Combine like terms for $m$
$3m + m = 4m$
## Step3: Combine results
$4m - 15$
# Answer: $4m - 15$

### Problem 4: $2s + 10 - 7s - 8 + 3s - 7$
# Explanation:
## Step1: Combine like terms for $s$
$2s - 7s + 3s = (2 - 7 + 3)s = -2s$
## Step2: Combine constant terms
$10 - 8 - 7 = -5$
## Step3: Combine results
$-2s - 5$
# Answer: $-2s - 5$

### Problem 5: $8c - 4 - 2c + 5$
# Explanation:
## Step1: Combine like terms for $c$
$8c - 2c = 6c$
## Step2: Combine constant terms
$-4 + 5 = 1$
## Step3: Combine results
$6c + 1$
# Answer: $6c + 1$

### Problem 6: $-4 + 7z + 3 - 2z$
# Explanation:
## Step1: Combine like terms for $z$
$7z - 2z = 5z$
## Step2: Combine constant terms
$-4 + 3 = -1$
## Step3: Combine results
$5z - 1$
# Answer: $5z - 1$

### Problem 7: $15 + 4(5y - 10)$
# Explanation:
## Step1: Distribute the 4
$4(5y - 10) = 20y - 40$
## Step2: Combine constant terms
$15 - 40 = -25$
## Step3: Combine results
$20y - 25$
# Answer: $20y - 25$

### Problem 8: $2d + 17 - 3 - 2d + 4d$
# Explanation:
## Step1: Combine like terms for $d$
$2d - 2d + 4d = 4d$
## Step2: Combine constant terms
$17 - 3 = 14$
## Step3: Combine results
$4d + 14$
# Answer: $4d + 14$

### Problem 9: $12n - 8 - 2n + 10 - 4$
# Explanation:
## Step1: Combine like terms for $n$
$12n - 2n = 10n$
## Step2: Combine constant terms
$-8 + 10 - 4 = -2$
## Step3: Combine results
$10n - 2$
# Answer: $10n - 2$

### Problem 10: $8(2k + 1 + 3k)$
# Explanation:
## Step1: Combine like terms inside the parentheses
$2k + 3k = 5k$, so inside is $5k + 1$
## Step2: Distribute the 8
$8(5k + 1) = 40k + 8$
# Answer: $40k + 8$

### Problem 11: $4(2b + 2) - 3$
# Explanation:
## Step1: Distribute the 4
$4(2b + 2) = 8b + 8$
## Step2: Combine constant terms
$8 - 3 = 5$
## Step3: Combine results
$8b + 5$
# Answer: $8b + 5$

### Problem 12: $-4 + 8p - 6p - 5 + 20p$
# Explanation:
## Step1: Combine like terms for $p$
$8p - 6p + 20p = 22p$
## Step2: Combine constant terms
$-4 - 5 = -9$
## Step3: Combine results
$22p - 9$
# Answer: $22p - 9$

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QUESTION IMAGE

Question

Explanation:

Problem 1: \(10x - 8x + 2 + 10\)

Step1: Combine like terms for \(x\)

Step2: Combine constant terms

Step3: Combine results

Step1: Distribute the 2

Step2: Combine like terms for \(a\)

Step3: Combine constant terms

Step4: Combine results

Step1: Distribute the 3

Step2: Combine like terms for \(m\)

Step3: Combine results

Answer:

Problem 2: \(3a + 7 + 2(3 + a)\)