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Chapter 0: Problem 101

Write each algebraic expression without parentheses. $$\frac{1}{3}(3 x)+[(4 y)+(-4 y)]$$

Short Answer

Expert verified
The simplified expression without parentheses is \(x\).

Step by step solution

01

Distribute the Fraction

Multiply the term outside the parentheses (\(\frac{1}{3}\)) with each term inside the parentheses (\(3x\)): \(\frac{1}{3} \cdot 3x = x\). So the first part of the expression simplifies to \(x\).
02

Simplify the Terms Inside the Brackets

Evaluate the terms inside the square brackets (\(4y + -4y\)) by adding up the like terms. This equals to 0 as they are same magnitude but opposite sign, so they cancel each other out.
03

Write the Final Expression

Combine the simplified parts obtained in step 1 and step 2 to write the final expression, which is \(x + 0\) or simply \(x\).

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Most popular questions from this chapter

Determine whether each statement in Exercises 43鈥�50 is true or false. $$0 \geq-13$$

Give an example of a rational number that is not an integer.

Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{2 x+3 y}{x+1}, \text { for } x=-2 \text { and } y=4$$

This will help you prepare for the material covered in the next section. a. Simplify: \(21 x+10 x\) b. Simplify: \(21 \sqrt{2}+10 \sqrt{2}\)

$$\text { Factor completely.}$$ $$3 x^{2}+5 x y^{2}+2 y^{4}$$
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