Problem 96 Simplify each expression. $$ ... [FREE SOLUTION]

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Chapter 1: Problem 96

Simplify each expression. $$ 0.06 x+0.14(x+200) $$

Short Answer

Expert verified

0.20x + 28

Step by step solution

- Distribute 0.14

Distribute the 0.14 to both terms inside the parenthesis. This gives: 0.14(x) + 0.14(200)

- Simplify the expression

Now, perform the multiplications: 0.14(x) = 0.14x 0.14(200) = 28

- Combine like terms

Combine the terms with x and the constants: 0.06x + 0.14x + 28

- Add coefficients of x

Combine the coefficients of x: (0.06 + 0.14)x = 0.20x

- Write the final expression

Putting it all together: 0.20x + 28

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Key Concepts

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

Distributive Property

The distributive property is a fundamental concept in algebra that allows you to simplify expressions where multiplication is distributed over addition or subtraction. For example, if you have the expression $a(b + c)$, you can use the distributive property to write it as $ab + ac$. This makes complex equations easier to handle.
In the exercise, you begin by distributing 0.14 to both terms inside the parenthesis:$ 0.14(x + 200) = 0.14(x) + 0.14(200)$. This step is essential because it transforms the expression into a simpler form.

Combining Like Terms

Combining like terms is another crucial algebraic skill. It involves consolidating terms that contain the same variable raised to the same power. This helps in simplifying expressions or solving equations.
Look at the terms $0.06x + 0.14x$. Both contain the variable $x$, making them 'like terms'. To simplify, you simply add the coefficients of the like terms. In this case, $0.06 + 0.14 = 0.20$, resulting in the simplified term $0.20x$. This step reduces the complexity of the expression and makes it easier to understand.

Coefficients in Algebra

In algebra, coefficients are the numerical factors that multiply variables. They play an essential role in the process of simplifying and solving equations.
For example, in $0.06x + 0.14(x + 200)$, the numbers 0.06 and 0.14 are coefficients of $x$. When you add or combine like terms, you are essentially working with these coefficients. In our exercise, after distributing 0.14, you combine the coefficients $0.06 + 0.14$ to find 0.20 as the new coefficient for $x$. This step simplifies your equation to its most concise form, $0.20x + 28$.
Understanding coefficients helps you navigate more complex algebraic structures with ease.

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91影视

Simplify each expression. $$ 0.06 x+0.14(x+200) $$

Short Answer

Step by step solution

- Distribute 0.14

- Simplify the expression

- Combine like terms

- Add coefficients of x

- Write the final expression

Key Concepts

Distributive Property

Combining Like Terms

Coefficients in Algebra

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