/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 37 \((3 x+15)+(4 x-9)\)... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 37

\((3 x+15)+(4 x-9)\)

Short Answer

Expert verified
7x + 6

Step by step solution

01

Remove the Parentheses

Write down the expression without the parentheses: (3x + 15) + (4x - 9) becomes 3x + 15 + 4x - 9.
02

Combine Like Terms

Identify and combine the like terms. Group the terms with x together and the constant terms together: (3x + 4x) + (15 - 9).
03

Simplify

Add the coefficients of x and the constants separately: 3x + 4x = 7x 15 - 9 = 6.
04

Final Answer

Combine the simplified terms to write the final expression: 7x + 6.

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Key Concepts

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

removing parentheses in algebra
When simplifying algebraic expressions, it's crucial to first remove any parentheses. Parentheses group parts of an expression. To simplify, you must remove them correctly.
Start by writing down the expression with parentheses: \((3x + 15) + (4x - 9)\).
When there are no signs outside the parentheses except addition, you can rewrite the expression without them. \(3x + 15 + 4x - 9\).
This step sets you up to combine like terms, the next part of simplifying expressions.
combining like terms
Combining like terms is the next step in simplifying algebraic expressions. Like terms are terms that have the same variables raised to the same power.
For example, in our expression, \(3x + 15 + 4x - 9\), both \(3x\) and \(4x\) are like terms.
The constants \(15\) and \(-9\) are also like terms.
  • Group the like terms together: \( (3x + 4x) + (15 - 9) \)
  • Add the coefficients of like terms separately.

Combining these terms simplifies the algebraic expression further, getting us closer to the final simplified form.
simplifying algebraic expressions
Simplifying algebraic expressions involves streamlining the equation to its simplest form. After removing parentheses and combining like terms, the next and final step is to simplify.
From the previous step, we have \( (3x + 4x) + (15 - 9) \).
  • Add the coefficients of \(x\): \( 3x + 4x = 7x \)
  • Subtract the constants: \ (15 - 9 = 6) \

The expression is now simplified to: \(7x + 6\).
By these steps, you have successfully removed parentheses, combined like terms, and finally simplified the algebraic expression to its simplest form.

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