Problem 17 Solve. $$ 4 x+7=3-5 x $$... [FREE SOLUTION]

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Chapter 15: Problem 17

Solve. $$ 4 x+7=3-5 x $$

Short Answer

Expert verified

x = $\frac{-4}{9}$

Step by step solution

Move all x terms to one side

Add $5x$ to both sides of the equation to combine the $x$ terms on one side. This gives us: $4x + 5x + 7 = 3$

Combine like terms

Combine the $x$ terms on the left side: $(4x + 5x) + 7 = 3$ which simplifies to: $9x + 7 = 3$

Move constant terms to the other side

Subtract 7 from both sides of the equation to isolate the $x$ term: $9x + 7 - 7 = 3 - 7$ which simplifies to: $9x = -4$

Solve for x

Divide both sides of the equation by 9 to solve for $x$: $x = \frac{-4}{9}$

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Key Concepts

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

Solving Equations

The process of solving equations is fundamentally about finding the value of the unknown variable that makes the equation true. In this exercise, we start with the equation 4x + 7 = 3 - 5x , and our goal is to determine the value of x . Solving an equation involves a series of carefully planned steps. You first move all terms involving the unknown to one side of the equation. Then, manage the constants or terms without the variable on the other side. The ultimate aim is to simplify the equation to a form where the variable stands alone on one side.

Algebraic Manipulation

Algebraic manipulation is crucial when working through solving equations. It refers to the steps and techniques used to simplify and rearrange an equation. Here鈥檚 a closer look at the steps for our given equation:

First, you add 5x to both sides to collect variable terms on one side: 4x + 5x + 7 = 3 + 0x
Next, combine like terms (4x + 5x) to get 9x + 7 = 3
Subtract 7 from both sides to isolate the term with the variable, yielding 9x = -4

This practice of collecting like terms and systematically moving terms from one side to another makes the equation simpler and easier to solve.

Isolating Variables

Isolating variables is the method by which we rearrange an equation to get the unknown variable on one side. For our equation, 9x + 7 = 3 , we isolated x by performing operations that progressively simplified the equation:

Firstly, subtracting 7 from both sides led to 9x = -4
Then, dividing both sides by 9 isolates x , giving us: x = -4/9
These steps demonstrate the principle of isolating variables, ensuring the unknown stands alone on one side of the equation, leading to the solution firmly.

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91影视

Solve. $$ 4 x+7=3-5 x $$

Short Answer

Step by step solution

Move all x terms to one side

Combine like terms

Move constant terms to the other side

Solve for x

Key Concepts

Solving Equations

Algebraic Manipulation

Isolating Variables

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