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Chapter 2: Problem 11

Solve each equation, and check your solution. $$ -5 z-4=21 $$

Short Answer

Expert verified
z = -5

Step by step solution

01

- Isolate the variable

Start by isolating the variable on one side of the equation. To do this, add 4 to both sides of the equation: -5z - 4 + 4 = 21 + 4
02

- Simplify both sides

Simplify the equation by combining like terms: -5z = 25
03

- Solve for the variable

Divide both sides by -5 to solve for z: \( z = \frac{25}{-5} \) z = -5
04

- Check the solution

Substitute z = -5 back into the original equation to verify your solution: -5(-5) - 4 = 21 25 - 4 = 21 21 = 21 The solution is correct.

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Key Concepts

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

isolate variable
To solve linear equations, the first core concept is to isolate the variable. Here, the variable is 'z'.
Start by moving any constants to the other side of the equation to simplify the process. In the provided exercise, the equation is -5z - 4 = 21.
By adding 4 to both sides, we aim to isolate 'z' on the left side:
-5z - 4 + 4 = 21 + 4

This simplifies to: -5z = 25.
The purpose of isolation is to make it easier to solve for the variable by itself.
combining like terms
The next important step while solving linear equations is combining like terms.
These are terms that have the same variable raised to the same power. In our equation from the previous step, we have: -5z = 25.

Since there's only one variable term here, there's no need to further combine like terms, but in other equations, you might see multiple z's and constants that need to be combined before proceeding. Ensuring all similar terms are grouped together will clarify the solution process.
verify solution
Verifying the solution is crucial to ensure the accuracy of your work.
In this case, our solution for 'z' is -5. Substituting z = -5 back into the original equation: -5(-5) - 4 should equal 21.

Let's check:
-5(-5) - 4 = 25 - 4 = 21.
This confirms that our solution is correct as both sides of the equation are equal.
Always take this step to catch any potential errors in your calculations.
educational methods in algebra
Understanding and implementing educational methods in algebra can vastly improve a student's ability to solve equations.
Core methods include:
  • Breaking down problems into smaller, manageable steps.
  • Using visual aids or graphing to conceptualize the problem.
  • Practicing consistently to build familiarity and confidence.

By incorporating these methods, students can grasp algebraic concepts more effectively and become proficient in solving equations like the one given.
Encouraging a methodical and patient approach will yield the best results.

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