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Chapter 1: Problem 37

Evaluate each of the following expressions, if possible. $$12-4(3-8)$$

Short Answer

Expert verified
The value is 32.

Step by step solution

01

- Evaluate inside the parentheses

To begin solving the expression, start by evaluating the expression within the parentheses \(3 - 8 = -5\).
02

- Substitute the result

Substitute \(-5\) into the original expression to get \(12 - 4(-5)\).
03

- Multiply

Next, multiply \(-4\) by \(-5\) to get \(12 - (-20)\).
04

- Simplify the expression

Finally, simplify \(12 - (-20)\). This becomes \(12 + 20 = 32\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Parentheses
When you see an expression with parentheses, always evaluate the inside first. Parentheses in math group parts of an expression. This helps you know which operations to do first. For example, in the expression \(12 - 4(3 - 8)\), you should first look at \(3 - 8\). Solve this part first before moving on.

Breaking it down:
  • Parentheses make it clear what to solve first.
  • They organize the expression.
  • Solve inside the parentheses before anything else.
So in our example, \(3 - 8 = -5\). Now you can move on to the rest of the expression.
Substitution in Algebra
Substitution means replacing a part of an expression with its value. Once you solve inside the parentheses, use substitution. Take the result and put it back into the original expression.

Here鈥檚 how it looks:
\(12 - 4(3 - 8)\) becomes \(12 - 4(-5)\) after substituting \( -5 \).

Steps for substitution:
  • Replace the solved part of the expression with its result.
  • Rewrite the whole expression with this new value.
  • Now go ahead and solve the rest of the expression.
By substituting \(-5\) into the expression, you now have \(12 - 4(-5)\).
Simplifying Expressions
Simplifying means making an expression easier to understand and solve. After substituting values into the expression, simplify it step by step. Make sure you follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

For the expression \(12 - 4(-5)\):
  • First, multiply: \(-4 \times -5 = 20\).
  • Rewrite the expression: \(12 - (-20)\).
  • Simplify: \(12 + 20 = 32\).
Each step brings you closer to the final answer. Following the correct order ensures you get the right solution.

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Most popular questions from this chapter

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