Problem 188 Solve the following equations wi... [FREE SOLUTION]

Chapter 2: Problem 188

Solve the following equations with variables on both sides. $$9 x+36=15 x$$

Short Answer

Expert verified

x = 6

Step by step solution

Combine like terms

We start by moving all the variable terms to one side of the equation. Subtract $9x$ from both sides of the equation: \[ 9x + 36 - 9x = 15x - 9x \] Simplifies to: \[ 36 = 6x \]

Solve for x

Isolate the variable by dividing both sides of the equation by 6: \[ \frac{36}{6} = \frac{6x}{6} \] Simplifies to: \[ x = 6 \]

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Key Concepts

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

Equations with variables on both sides

When solving equations with variables on both sides, the goal is to consolidate all variable terms on one side of the equation and all constant terms on the other. This will often involve moving terms by addition or subtraction. For example, in the equation $9x + 36 = 15x$, our first step is to get all the x terms on the same side.

We can do this by subtracting $9x$ from both sides, which gives us: \[ 9x + 36 - 9x = 15x - 9x \]

Simplifying this results in: \[ 36 = 6x \]

Now, the equation has become a simpler problem to solve as all x terms are on one side.

Combining like terms

Combining like terms is a key step in simplifying and solving equations. Terms that contain the same variable can be added or subtracted from one another. In our example: \[ 9x + 36 = 15x \]

We combine like terms by moving $9x$ to the same side as $15x$ through subtraction:

\[ 9x + 36 - 9x = 15x - 9x \]

This simplifies to: \[ 36 = 6x \]

Here, we've combined $15x - 9x$ to get $6x$. This makes it easier to solve the equation, as it is now in a simpler form with fewer terms.

Isolating the variable

Isolating the variable is the final step to find the value of x (or any variable). The goal is to have the variable on one side of the equation by itself. In our example, after simplifying the equation to \[ 36 = 6x \], we need to isolate $x$.

To do this, we divide both sides of the equation by the coefficient of $x$, which is 6:

\[ \frac{36}{6} = \frac{6x}{6} \]

Simplifying this results in: \[ x = 6 \]

Now, we have isolated $x$ and found that $x = 6$. This process of isolating the variable is key to solving linear equations.

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91影视

Solve the following equations with variables on both sides. $$9 x+36=15 x$$

Short Answer

Step by step solution

Combine like terms

Solve for x

Key Concepts

Equations with variables on both sides

Combining like terms

Isolating the variable

One App. One Place for Learning.

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