Problem 9 Solve each equation, and check t... [FREE SOLUTION]

Chapter 2: Problem 9

Solve each equation, and check the solution. \(-5 z-4=21\)

Short Answer

Expert verified

The solution is \( z = -5 \).

Step by step solution

Isolate the variable term

Add 4 to both sides of the equation to begin isolating the variable term. -5z - 4 + 4 = 21 + 4 This simplifies to -5z = 25

Solve for the variable

Divide both sides of the equation by -5 to solve for z. \( z = \frac{25}{-5} \) This simplifies to \( z = -5 \)

Check the solution

Substitute the solution back into the original equation to verify it. -5(-5) - 4 = 21 Simplifies to 25 - 4 = 21 Which is true since 21 = 21

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Key Concepts

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

Isolate the Variable

To solve a linear equation, the first step is to isolate the variable. This means getting the variable by itself on one side of the equation.

In the equation \( -5z - 4 = 21 \), we start by adding 4 to both sides.

This step counteracts the \( -4 \) that is subtracted from \(-5z\).
So, \( -5z - 4 + 4 = 21 + 4 \).
This simplifies to \( -5z = 25 \).

By isolating the variable term \( -5z \), we have made the equation simpler and prepared it for the next step.

Remember, whatever operation you perform on one side of the equation, you must do the same to the other side. This keeps the equation balanced.

Substitution Method

Once we isolate the variable, we use the substitution method to find its value.

In the equation \( -5z = 25 \), we solve for \( z \) by dividing both sides by -5.

This removes the coefficient of \( z \).
So, we have \( z = \frac{25}{-5} \).
When simplified, it gives us \( z = -5 \).

At this stage, we have found the value of \( z \). It's important to be careful with signs when performing division or multiplication.

Check the Solution

After solving for the variable, it's crucial to check if the solution is correct.

To do this, substitute the value back into the original equation.

For our equation \( -5z - 4 = 21 \), we substitute \( z = -5 \):

Replace \( z \) with -5, giving us \( -5(-5) - 4 \).
Calculate: \( -5(-5) = 25 \).
Then, \( 25 - 4 \) simplifies to 21.
This matches the original right side of the equation: \( 21 = 21 \).

By successfully verifying that both sides are equal, we confirm our solution \( z = -5 \) is correct. This step ensures the work and solution are accurate.

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91影视

Solve each equation, and check the solution. \(-5 z-4=21\)

Short Answer

Step by step solution

Isolate the variable term

Solve for the variable

Check the solution

Key Concepts

Isolate the Variable

Substitution Method

Check the Solution

One App. One Place for Learning.

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