Find the value of each of the following algebraic expressions.
ab- 3b + 7c, where a = 5, b = 7, c = 4

Answer

To find the value of the algebraic expression \( ab - 3b + 7c \) where \( a = 5 \), \( b = 7 \), and \( c = 4 \), we will follow these steps:

### Step 1: Substitute the values of \( a \), \( b \), and \( c \) into the expression.
The expression is:
\[ ab - 3b + 7c \]
Substituting the values:
\[ (5)(7) - 3(7) + 7(4) \]

### Step 2: Calculate \( ab \).
Now, calculate \( ab \):
\[ 5 \times 7 = 35 \]
So, we have:
\[ 35 - 3(7) + 7(4) \]

### Step 3: Calculate \( -3b \).
Next, calculate \( -3b \):
\[ -3 \times 7 = -21 \]
Now the expression looks like:
\[ 35 - 21 + 7(4) \]

### Step 4: Calculate \( 7c \).
Now, calculate \( 7c \):
\[ 7 \times 4 = 28 \]
So, we have:
\[ 35 - 21 + 28 \]

### Step 5: Combine the values.
Now, combine the values:
\[ 35 - 21 = 14 \]
Then add \( 28 \):
\[ 14 + 28 = 42 \]

### Final Answer:
The value of the expression \( ab - 3b + 7c \) is \( 42 \).

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