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Chapter 1: Problem 72

Simplify each expression. $$ 9-(w-5) $$

Short Answer

Expert verified
14 - w

Step by step solution

01

- Distribute the negative sign

Start by distributing the negative sign across the expression within the parentheses. This means to apply the negative sign to both terms inside the parentheses: 9 - (w - 5) = 9 - w + 5}
02

- Combine like terms

Next, combine the constant terms (9 and 5): 9 - w + 5 = (9 + 5) - w}
03

- Simplify

Finally, simplify the addition of the constants: (9 + 5) - w = 14 - w}

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Key Concepts

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

Distributing Negative Sign
When you need to simplify expressions, especially those involving parentheses, pay special attention to the negative sign. In the expression 9 - (w - 5), the negative sign in front of the parentheses means that you need to distribute or apply this negative sign to every term inside the parentheses.
This changes the sign of each term:
  • - (w) becomes -w
  • - (-5) becomes +5

Applying this to our expression, we get: 9 - (w - 5) becomes 9 - w + 5.
Once you have successfully distributed the negative sign, you can move on to the next step.
Combining Like Terms
After distributing the negative sign, the next step is to combine like terms. 'Like terms' are terms that contain the same variables raised to the same power. In our example, after distributing, we have: 9 - w + 5.

The terms 9 and 5 are constants, meaning they do not contain any variables. These constants can be easily combined by simple addition:
  • Combine 9 and 5 to get 14.

Now, our expression becomes: 14 - w.
Combining like terms helps in simplifying the expression, making it easier to understand and work with.
Constants in Algebra
Constants are numbers on their own without any variable attached to them. In our expression 9 - (w - 5), the numbers 9 and 5 are constants.

Understanding how to deal with constants is essential for simplifying any algebraic expression:
  • Add or subtract constants just like regular numbers
  • Remember, constants do not change as they have no variables

This allows you to combine them quickly and simplify expressions, just as we did by combining 9 and 5 to get 14 in the simplified expression: 14 - w.
Working with constants efficiently can greatly simplify your problems in algebra.

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Most popular questions from this chapter

Write an algebraic expression for each problem. Parthenon. To obtain a pleasing rectangular shape, the ancient Greeks constructed buildings with a length that was about \(\frac{1}{6}\) longer than the width. If the width of the Parthenon is \(x\) meters and its length is \(x+\frac{1}{6} x\) meters, then what is the perimeter? What is the area?

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