/*! 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 88 \(-5(3 w-3)+(16 w+1)=0\)... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 88

\(-5(3 w-3)+(16 w+1)=0\)

Short Answer

Expert verified
w = -16

Step by step solution

01

- Distribute the -5

First, distribute the -5 across the terms inside the parentheses:-5(3w - 3) = -15w + 15
02

- Rewrite the equation

Rewrite the equation using the result from Step 1:-15w + 15 + 16w + 1 = 0
03

- Combine like terms

Combine the like terms (-15w and 16w):w + 16 = 0
04

- Solve for w

Subtract 16 from both sides:w = -16

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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 crucial concept in algebra. It allows you to multiply a single term by each term within a set of parentheses. In the given equation, we need to apply the distributive property to -5(3w - 3). This means we'll multiply -5 by 3w and by -3. The multiplication yields -15w, since -5 multiplied by 3w is -15w. Similarly, -5 multiplied by -3 is 15. So the expression -5(3w - 3) becomes -15w + 15. Understanding and applying the distributive property is essential for simplifying and solving linear equations.
Combining Like Terms
Once you've applied the distributive property, the next step is to combine like terms. Like terms are terms that have the same variable raised to the same power. In the rewritten equation -15w + 15 + 16w + 1 = 0, we can see the terms -15w and 16w are like terms because they both contain the variable w. By combining these, we get -15w + 16w, which simplifies to w. Similarly, we also combine the constant terms 15 and 1 to get 16. Combining like terms helps to further simplify the equation, making it easier to solve.
Isolating the Variable
The final step in solving the equation is to isolate the variable w. This means getting w on one side of the equation by itself. In the simplified equation, we now have w + 16 = 0. To isolate w, we need to move the 16 to the other side of the equation. We do this by subtracting 16 from both sides, giving us w = -16. Isolating the variable is the ultimate goal in solving linear equations as it allows us to find the value of the variable that satisfies the equation.

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