Evaluate the expression -3(4b - a) given a = 12 and b = 5.

Understand the Problem

The question is asking us to evaluate the mathematical expression -3(4b - a) using the given values of a and b, which are 12 and 5, respectively. We will substitute these values into the expression and simplify it to get the final result.

Answer

The final result of the expression is $-24$.

Steps to Solve

Substituting values into the expression

First, substitute the values of (a) and (b) into the expression. Given (a = 12) and (b = 5), we write:

$$ -3(4b - a) = -3(4(5) - 12) $$

Calculating the multiplication inside the parentheses

Next, calculate (4b):

$$ 4(5) = 20 $$

Now substitute this back into the expression:

$$ -3(20 - 12) $$

Performing the subtraction inside the parentheses

Now perform the subtraction:

$$ 20 - 12 = 8 $$

So the expression now becomes:

$$ -3(8) $$

Calculating the final multiplication

Finally, multiply -3 by 8:

$$ -3 \times 8 = -24 $$

The final answer is -24.

More Information

The expression evaluated to -24 shows that when we substitute the given values and simplify, we follow the rules of order of operations carefully. This result illustrates how negative multiplications work, giving a negative outcome.

Tips

Forgetting to distribute the negative sign when multiplying.
Failing to correctly substitute values into the expression.
Miscalculating multiplication or basic arithmetic operations.

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