Problem 41 Solve each equation, and check y... [FREE SOLUTION]

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Chapter 2: Problem 41

Solve each equation, and check your solution. $$ 5.6 x+2=4.6 x $$

Short Answer

Expert verified

x = -2

Step by step solution

- Move all terms involving x to one side

Subtract $4.6x$ from both sides of the equation: $5.6x + 2 - 4.6x = 4.6x - 4.6x$

- Simplify the equation

Combine like terms: $1.0x + 2 = 0$. This simplifies to $x + 2 = 0$

- Isolate x

Subtract 2 from both sides to isolate $x$: $x = -2$

- Check the solution

Substitute $x = -2$ back into the original equation: $5.6(-2) + 2 = 4.6(-2)$.Evaluate both sides:$ -11.2 + 2 = -9.2$ on the left and $-9.2$ on the right making both sides equal $-9.2 = -9.2$

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Key Concepts

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

Isolate the Variable

When solving linear equations, our main goal is to find the value of the variable. The first step you usually take is to isolate the variable on one side of the equation.
To isolate the variable means to get it by itself. You do this by performing operations that cancel out other terms on the same side as the variable.
Let's look at the equation from the exercise:
5.6x + 2 = 4.6x
Here, both sides have terms that involve the variable x. We need to move all the terms involving x to one side of the equation.
To do this, we subtract 4.6x from both sides:
5.6x + 2 - 4.6x = 4.6x - 4.6x
Now, we combine the terms to continue simplifying the equation.

Combine Like Terms

Combining like terms is an essential step when working to simplify an equation. Like terms are terms that contain the same variable raised to the same power.
In our exercise, after subtracting 4.6x from both sides, we get:
1.0x + 2 = 0
Here, 1.0x and 2 are our terms. We combine these terms to make the equation even simpler:
x + 2 = 0
Combining the like terms helps us see more clearly what needs to be done next. The last thing we'll need to do is...

Check Solutions

After solving for the variable, it's crucial to check your solution. This step ensures you didn't make any mistakes. In our example, we found that x = -2.
To check the solution, we substitute x = -2 back into the original equation.
5.6(-2) + 2 = 4.6(-2)
Now, let's do the math on both sides of the equation:
-11.2 + 2 = -9.2
-9.2 = -9.2
Both sides of the equation are equal, confirming our solution x = -2 is correct. This verification step makes sure our solution satisfies the original equation.

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91影视

Solve each equation, and check your solution. $$ 5.6 x+2=4.6 x $$

Short Answer

Step by step solution

- Move all terms involving x to one side

- Simplify the equation

- Isolate x

- Check the solution

Key Concepts

Isolate the Variable

Combine Like Terms

Check Solutions

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