simplify the expression.
4. $4h - 8h$
5. $6.4r - 7 - 2.9r$
6. $\frac{3}{5}x + 19 - \frac{3}{20}x - 7$
7. $3(2 + q) + 15$
8. $\frac{1}{8}(16m - 8) - 17$
9. $-1.5(4 - n) + 2.8$

Question

Accepted Answer

### Problem 4: Simplify $ 4h - 8h $
# Explanation:
## Step 1: Combine like terms
Like terms have the same variable. Here, $ 4h $ and $ -8h $ are like terms. Subtract the coefficients: $ 4 - 8 = -4 $.
So, $ 4h - 8h = -4h $.
# Answer: $ -4h $

### Problem 5: Simplify $ 6.4r - 7 - 2.9r $
# Explanation:
## Step 1: Combine like terms for $ r $
$ 6.4r $ and $ -2.9r $ are like terms. Subtract their coefficients: $ 6.4 - 2.9 = 3.5 $.
## Step 2: Write the simplified form
The constant term $ -7 $ remains. So, $ 6.4r - 2.9r - 7 = 3.5r - 7 $.
# Answer: $ 3.5r - 7 $

### Problem 6: Simplify $ \frac{3}{5}x + 19 - \frac{3}{20}x - 7 $
# Explanation:
## Step 1: Combine like terms for $ x $
First, find a common denominator for $ \frac{3}{5}x $ and $ -\frac{3}{20}x $. The common denominator of 5 and 20 is 20. Convert $ \frac{3}{5}x $ to $ \frac{12}{20}x $. Then subtract: $ \frac{12}{20}x - \frac{3}{20}x = \frac{9}{20}x $.
## Step 2: Combine constant terms
$ 19 - 7 = 12 $.
## Step 3: Write the simplified form
Combine the results: $ \frac{9}{20}x + 12 $.
# Answer: $ \frac{9}{20}x + 12 $

### Problem 7: Simplify $ 3(2 + q) + 15 $
# Explanation:
## Step 1: Distribute the 3
Multiply 3 by each term inside the parentheses: $ 3 \times 2 = 6 $ and $ 3 \times q = 3q $. So, $ 3(2 + q) = 6 + 3q $.
## Step 2: Combine like terms
Add 6 and 15: $ 6 + 15 = 21 $.
## Step 3: Write the simplified form
So, $ 6 + 3q + 15 = 3q + 21 $.
# Answer: $ 3q + 21 $

### Problem 8: Simplify $ \frac{1}{8}(16mn - 8) - 17 $
# Explanation:
## Step 1: Distribute $ \frac{1}{8} $
Multiply $ \frac{1}{8} $ by each term inside the parentheses: $ \frac{1}{8} \times 16mn = 2mn $ and $ \frac{1}{8} \times (-8) = -1 $. So, $ \frac{1}{8}(16mn - 8) = 2mn - 1 $.
## Step 2: Subtract 17
Subtract 17 from $ 2mn - 1 $: $ 2mn - 1 - 17 = 2mn - 18 $.
# Answer: $ 2mn - 18 $

### Problem 9: Simplify $ -1.5(4 - n) + 2.8 $
# Explanation:
## Step 1: Distribute $ -1.5 $
Multiply $ -1.5 $ by each term inside the parentheses: $ -1.5 \times 4 = -6 $ and $ -1.5 \times (-n) = 1.5n $. So, $ -1.5(4 - n) = -6 + 1.5n $.
## Step 2: Add 2.8
Add 2.8 to $ -6 + 1.5n $: $ -6 + 2.8 + 1.5n = -3.2 + 1.5n $ (or $ 1.5n - 3.2 $).
# Answer: $ 1.5n - 3.2 $ (or $ -3.2 + 1.5n $)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 4: Simplify \( 4h - 8h \)

Step 1: Combine like terms

Step 1: Combine like terms for \( r \)

Step 2: Write the simplified form

Step 1: Combine like terms for \( x \)

Step 2: Combine constant terms

Step 3: Write the simplified form

Answer:

Problem 5: Simplify \( 6.4r - 7 - 2.9r \)