To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will apply the order of operations, commutative and distributive properties. Here's a step-by-step breakdown:
-
Apply the Distributive Property: First, we need to distribute \( 8 \) to each term inside the parentheses \( (3x - 2) \):
\[ 8(3x) - 8(2) = 24x - 16 \]
So the expression now looks like this:
\[ 4 + (24x - 16) - 7x \]
-
Combine Like Terms: Next, we will rewrite the expression, correctly grouping it for easier simplification:
\[ 4 - 16 + 24x - 7x \]
Now, we can combine the like terms. First, handle the constant terms:
\[ 4 - 16 = -12 \]
Next, combine the \( x \) terms:
\[ 24x - 7x = 17x \]
-
Final Result: Now, we can write the simplified expression by combining all the results:
\[ -12 + 17x \]
This is typically written in standard form (with the variable term first):
\[ 17x - 12 \]
Thus, the simplified expression is:
\[ \boxed{17x - 12} \]
1 answer