/*! 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 255 Solve each linear equation. $$... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 255

Solve each linear equation. $$15-(3 r+8)=28$$

Short Answer

Expert verified
r = -7

Step by step solution

01

Distribute and combine like terms

Rewrite the equation removing the parentheses. Subtract terms inside the parentheses: 15 - 3r - 8 = 28 Simplify the left side by combining the constants: 15 - 8 = 7 This gives us:7 - 3r = 28
02

Isolate the variable term

To get 3r alone on one side, subtract 7 from both sides of the equation: 7 - 3r = 28 -7 -7 Resulting in:-3r = 21
03

Solve for r

To solve for r, divide both sides by -3: -3r / -3 = 21 / -3 This simplifies to: r = -7

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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 principle in algebra. It allows us to remove parentheses by multiplying the term outside the parentheses with each term inside. Consider the given problem: $$15 - (3r + 8) = 28$$First, remove the parentheses by distributing the subtraction (which is like multiplying by -1) to both terms inside:$$15 - 3r - 8 = 28$$This step helps to simplify the equation and prepares it for the next phase, where we鈥檒l combine like terms.
Combining Like Terms
Combining like terms means grouping and simplifying terms that have the same variable. In our simplified equation from the previous step:$$15 - 3r - 8 = 28$$Observe the constants (numbers without variables): 15 and -8. Combine these constants by performing the arithmetic:$$15 - 8 = 7$$Now, the equation looks simpler:$$7 - 3r = 28$$This makes it easier to isolate the variable term in the subsequent steps, as it reduces complexity and helps focus on the variable part of the equation.
Isolating Variables
Isolating the variable means getting the variable (here, 'r') by itself on one side of the equation. Starting with the simplified equation:$$7 - 3r = 28$$First, subtract 7 from both sides to move the constant away from the variable term:$$7 - 3r - 7 = 28 - 7$$This simplifies to:$$-3r = 21$$Now, to isolate 'r', divide both sides by -3:\frac{-3r}{-3} = \frac{21}{-3}Simplifying this gives us:$$r = -7$$The variable 'r' is now isolated, and we have our solution. Isolating variables is crucial for solving equations because it helps find the exact value of the unknown variable.

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