Problem 96 Solve \(5-3(x-9)+4 x=3(x-8)-2(x+... [FREE SOLUTION]

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Precalculus Functions and Graphs

Mark Dugopolski

$Math Studyset 91影视 Explanations$ Math

4 Edition

Chapter 11: Problem 96

Solve $5-3(x-9)+4 x=3(x-8)-2(x+1)$

Short Answer

Expert verified

Combine like terms to get x = 22.

Step by step solution

- Distribute the constants

Distribute the constants inside the parentheses: 5 - 3(x - 9) + 4x = 3(x - 8) - 2(x + 1). This simplifies to: 5 - 3x + 27 + 4x = 3x - 24 - 2x - 2.

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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 key concept in algebra that helps simplify expressions and solve equations. It states that for any numbers a, b, and c, the expression $a(b + c)$ is equivalent to $ab + ac$. This property allows you to 鈥榙istribute鈥� the multiplication of a number across terms inside a parenthesis.For example, in the exercise, $-3(x - 9)$ becomes $-3x + 27$, and $4x$ remains $4x$ because there is no parenthesis. On the other side of the equation, $3(x - 8)$ translates to $3x - 24$, and $-2(x+1)$ simplifies to $-2x - 2$. By distributing constants inside parentheses, you simplify the problem and make it easier to handle.

Linear Equations

Linear equations are algebraic equations in which each term is either a constant or the product of a constant and a single variable. These equations look like a straight line when graphed on a coordinate plane. Examples of linear equations include $y = 2x + 3$ and $5x - 7 = 18$.In our exercise, once we distribute and simplify, we have a linear equation that should look something like this: $-3x + 27 + 4x = 3x - 24 - 2x$. The goal is to isolate the variable (in this case, x) on one side and the constants on the other. It leads us to understand how two expressions relate and can be equal to one another.

Simplification

Simplification involves combining like terms and making the equation easier to solve. Once you distribute the constants in the exercise, you have terms that you can combine. These are terms that have the same variable or are constants.For instance, with $-3x + 27 + 4x$, we combine like terms. $-3x + 4x$ becomes $x$, and we get $x + 27$. On the other side, $3x - 2x$ simplifies to $x$, giving us $x - 26$. By combining these like terms, we bring the equation down to its simplest form, making it easier to see the solution.Understanding simplification helps you solve equations more efficiently and makes complex problems easier to manage.

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91影视

Solve \(5-3(x-9)+4 x=3(x-8)-2(x+1)\)

Short Answer

Step by step solution

- Distribute the constants

Key Concepts

Distributive Property

Linear Equations

Simplification

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