algebra concepts chapter 6 evaluating expressions mastery check
1. 6.1 evaluate 6p - 5 when p = -4.
2. 6.1 evaluate -h - 9 when h = -3.
3. 6.2 evaluate 5pq - 6r when p = -2, q = 3 and r = 9.
4. 6.3 evaluate -v² when v = -7.
5. 6.3 evaluate -2h² - 8h + 6 when h = -9.
6. 6.4 evaluate $\frac{5}{3}x + 4$ when x = -12.

Question

Accepted Answer

### Problem 1: Evaluate $ 6p - 5 $ when $ p = -4 $
# Explanation:
## Step 1: Substitute $ p = -4 $ into the expression
Substitute $ p = -4 $ into $ 6p - 5 $, we get $ 6(-4) - 5 $.
## Step 2: Calculate the multiplication first
Calculate $ 6(-4) = -24 $.
## Step 3: Calculate the subtraction
Now, $ -24 - 5 = -29 $.
# Answer: $ -29 $

### Problem 2: Evaluate $ -h - 9 $ when $ h = -3 $
# Explanation:
## Step 1: Substitute $ h = -3 $ into the expression
Substitute $ h = -3 $ into $ -h - 9 $, we get $ -(-3) - 9 $.
## Step 2: Simplify the double negative
$ -(-3) = 3 $, so the expression becomes $ 3 - 9 $.
## Step 3: Calculate the subtraction
$ 3 - 9 = -6 $.
# Answer: $ -6 $

### Problem 3: Evaluate $ 5pq - 6r $ when $ p = -2 $, $ q = 3 $ and $ r = 9 $
# Explanation:
## Step 1: Substitute the values into the expression
Substitute $ p = -2 $, $ q = 3 $, $ r = 9 $ into $ 5pq - 6r $, we get $ 5(-2)(3) - 6(9) $.
## Step 2: Calculate the multiplications
First, $ 5(-2)(3) = -30 $, and $ 6(9) = 54 $.
## Step 3: Calculate the subtraction
Now, $ -30 - 54 = -84 $.
# Answer: $ -84 $

### Problem 4: Evaluate $ -v^2 $ when $ v = -7 $
# Explanation:
## Step 1: Substitute $ v = -7 $ into the expression
Substitute $ v = -7 $ into $ -v^2 $, we get $ -(-7)^2 $.
## Step 2: Calculate the exponent first
Calculate $ (-7)^2 = 49 $.
## Step 3: Apply the negative sign
Now, $ -49 $.
# Answer: $ -49 $

### Problem 5: Evaluate $ -2h^2 - 8h + 6 $ when $ h = -9 $
# Explanation:
## Step 1: Substitute $ h = -9 $ into the expression
Substitute $ h = -9 $ into $ -2h^2 - 8h + 6 $, we get $ -2(-9)^2 - 8(-9) + 6 $.
## Step 2: Calculate the exponent
Calculate $ (-9)^2 = 81 $, so the expression becomes $ -2(81) - 8(-9) + 6 $.
## Step 3: Calculate the multiplications
$ -2(81) = -162 $ and $ -8(-9) = 72 $.
## Step 4: Calculate the addition and subtraction
Now, $ -162 + 72 + 6 = -84 $.
# Answer: $ -84 $

### Problem 6: Evaluate $ \frac{5}{3}x + 4 $ when $ x = -12 $
# Explanation:
## Step 1: Substitute $ x = -12 $ into the expression
Substitute $ x = -12 $ into $ \frac{5}{3}x + 4 $, we get $ \frac{5}{3}(-12) + 4 $.
## Step 2: Calculate the multiplication
Calculate $ \frac{5}{3}(-12) = -20 $.
## Step 3: Calculate the addition
Now, $ -20 + 4 = -16 $.
# Answer: $ -16 $

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QUESTION IMAGE

Question

Explanation:

Problem 1: Evaluate \( 6p - 5 \) when \( p = -4 \)

Step 1: Substitute \( p = -4 \) into the expression

Step 2: Calculate the multiplication first

Step 3: Calculate the subtraction

Step 1: Substitute \( h = -3 \) into the expression

Step 2: Simplify the double negative

Step 3: Calculate the subtraction

Step 1: Substitute the values into the expression

Step 2: Calculate the multiplications

Step 3: Calculate the subtraction

Answer:

Problem 2: Evaluate \( -h - 9 \) when \( h = -3 \)