Problem 70 Solve each equation, and check t... [FREE SOLUTION]

Chapter 2: Problem 70

Solve each equation, and check the solution. $$ -5 x+4 x-8 x=0 $$

Short Answer

Expert verified

The solution is x = 0. Checking confirms that both sides of the equation are equal.

Step by step solution

Combine Like Terms

First combine the like terms on the left-hand side of the equation: -5x + 4x - 8x. This simplifies to -9x because -5 + 4 = -1 and -1 - 8 = -9. So, the equation becomes: -9x = 0.

Solve for x

To solve for x, divide both sides of the equation by -9: x = 0. Therefore, the solution to the equation is x = 0.

Check the Solution

Substitute x = 0 back into the original equation to check the solution: -5(0) + 4(0) - 8(0) = 0. Simplifying both sides: 0 = 0. The solution is correct as both sides of the equation are equal.

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Key Concepts

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

combining like terms

When solving linear equations, the first step is often to combine like terms. Like terms are terms that have the same variable raised to the same power. In our example, the equation is -5x + 4x - 8x = 0. All of these terms are 'like' because they all contain the variable 'x'.

Combining these like terms means adding or subtracting their coefficients (the numbers in front of the variables).

Here, we start with -5x + 4x - 8x. First, combine -5 and 4 which gives us -1. So now, we have -1x - 8x. Next, combine -1 and -8 to get -9. This simplifies our equation to -9x = 0. Combining like terms simplifies equations, making them easier to solve in the subsequent steps.

simplifying equations

Once like terms are combined, we aim to simplify the equation further to make solving for the variable easier. Simplifying an equation often involves isolating the variable on one side of the equation.

In our example, after combining like terms, the equation became -9x = 0. To isolate 'x', we need to get rid of the coefficient -9. We do this by dividing both sides of the equation by -9.

Performing the division, we get: \[ x = \frac{0}{-9} \] which simplifies to x = 0. Simplifying equations by isolating the variable helps in finding the value of the variable more directly and clearly.

checking solutions

To ensure our solution is correct, it is crucial to check it by substituting the value back into the original equation. This helps verify that both sides of the equation are equal.

Let's check our solution for x = 0. We substitute x = 0 back into the original equation: -5x + 4x - 8x = 0. Replacing x with 0, we get: -5(0) + 4(0) - 8(0) = 0. Simplifying the left side, we have 0 + 0 + 0 = 0. Since both sides of the equation equal 0, the solution x = 0 is correct.

Always check your solutions to confirm their accuracy. This step ensures the solution truly satisfies the original equation and no mistakes were made during the process.

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91影视

Solve each equation, and check the solution. $$ -5 x+4 x-8 x=0 $$

Short Answer

Step by step solution

Combine Like Terms

Solve for x

Check the Solution

Key Concepts

combining like terms

simplifying equations

checking solutions

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