Certainly! Let's break down the given mathematical expression \( 8(10 - 6q) + 3(-7q - 2) \) step-by-step.
### Step 1: Distribute the 8 through the first set of parentheses
First, we distribute the 8 to both terms inside the parentheses \( 10 \) and \( -6q \).
[tex]\[ 8 \cdot 10 = 80 \][/tex]
[tex]\[ 8 \cdot (-6q) = -48q \][/tex]
So, the first part becomes:
[tex]\[ 8(10 - 6q) = 80 - 48q \][/tex]
### Step 2: Distribute the 3 through the second set of parentheses
Next, we distribute the 3 to both terms inside the parentheses \( -7q \) and \( -2 \).
[tex]\[ 3 \cdot (-7q) = -21q \][/tex]
[tex]\[ 3 \cdot (-2) = -6 \][/tex]
So, the second part becomes:
[tex]\[ 3(-7q - 2) = -21q - 6 \][/tex]
### Step 3: Combine the results
Now, let’s add these distributed parts together:
[tex]\[ 80 - 48q + (-21q - 6) \][/tex]
### Step 4: Combine like terms
Finally, we combine the like terms. Combine the constants \( 80 \) and \( -6 \), and combine the coefficients of \( q \), which are \( -48q \) and \( -21q \):
[tex]\[ 80 - 6 = 74 \][/tex]
[tex]\[ -48q - 21q = -69q \][/tex]
Putting it all together, the simplified expression is:
[tex]\[ 74 - 69q \][/tex]
So the equivalent expression for \( 8(10 - 6q) + 3(-7q - 2) \) is:
[tex]\[ 74 - 69q \][/tex]
