Problem 122 Combine like terms. $$ 8 t-(... [FREE SOLUTION]

Chapter 1: Problem 122

Combine like terms. $$ 8 t-(-2 t)-14-(-5 t)+53-9 t $$

Short Answer

Expert verified

$6t + 39$

Step by step solution

Distribute the Negatives

Start by removing the parentheses and distributing the negative signs: $8t - (-2t) - 14 - (-5t) + 53 - 9t $ becomes $8t + 2t - 14 + 5t + 53 - 9t$.

Combine Like Terms (t-terms)

Next, combine the terms involving $t$: $8t + 2t + 5t - 9t = (8 + 2 + 5 - 9)t = 6t$.

Combine Like Terms (Constant terms)

Now, combine the constant terms: $ -14 + 53 = 39$.

Write the Final Expression

Combine the results from Step 2 and Step 3 to obtain the final simplified expression: $6t + 39$.

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Key Concepts

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

Distribution of Negatives

When you encounter an algebraic expression with negative signs, you need to distribute them correctly. Removing parentheses is crucial. For instance, in the expression $8t - (-2t) - 14 - (-5t) + 53 - 9t$, notice how the negative signs are in front of parentheses. To remove the parentheses and distribute the negatives, you change the signs inside.

Here鈥檚 a simple way to think about it:

$-(-2t)$ turns into $+2t$
$-(-5t)$ turns into $+5t$

So the expression $8t - (-2t) - 14 - (-5t) + 53 - 9t$ becomes $8t + 2t - 14 + 5t + 53 - 9t$. This step makes further simplification easier.

Simplification

Once the negative signs are correctly distributed, you can focus on combining like terms. Combining like terms involves grouping and adding or subtracting the coefficients of the same variable.

For the expression $8t + 2t - 14 + 5t + 53 - 9t$, start by looking at the terms with the variable $t$. These are:

$8t$
$+2t$
$+5t$
$-9t$

Add the coefficients together: $8 + 2 + 5 - 9$. This simplifies to $6t$.

Next, look at the constant terms:

$-14$
$+53$

Simplify by adding them: $-14 + 53 = 39$.
Finally, combine the simplified like terms: $6t + 39$. Now you have a simplified expression.

Algebraic Expressions

Understanding algebraic expressions is key to mastering algebra. An algebraic expression consists of variables, coefficients, and constants:

Variables (like $t$ in our example) represent unknown values.
Coefficients (numbers in front of variables) are the numeric part of a term.
Constants are standalone numbers (like $-14$ and $+53$).

To solve or simplify algebraic expressions:
Distribute any negative signs or perform any multiplications/divisions needed. Combine like terms: add or subtract the coefficients of the same variable. Simplify the constants by performing any addition or subtraction.

For example, in our exercise, after distributing the negatives and combining like terms, we ended up with $6t + 39$. Understanding these steps ensures you handle any similar problem with ease.

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91影视

Combine like terms. $$ 8 t-(-2 t)-14-(-5 t)+53-9 t $$

Short Answer

Step by step solution

Distribute the Negatives

Combine Like Terms (t-terms)

Combine Like Terms (Constant terms)

Write the Final Expression

Key Concepts

Distribution of Negatives

Simplification

Algebraic Expressions

One App. One Place for Learning.

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