Introduction
In this article, we will be providing the step-by-step solutions for Lesson 14 Homework 5.4. This answer key will help you check your work and ensure that you have understood the concepts covered in this lesson. By following along with the solutions provided, you will be able to identify any mistakes and learn from them. So, let’s dive in and explore the answer key for Lesson 14 Homework 5.4!
Lesson 14: Homework 5.4 Answer Key – Step-by-Step Solutions
Question 1:
To solve this question, we need to find the value of x that satisfies the equation 3x + 5 = 14.
Step 1: Start by subtracting 5 from both sides of the equation to isolate the term with x. This gives us 3x = 14 – 5 = 9.
Step 2: Next, divide both sides of the equation by 3 to solve for x. This gives us x = 9/3 = 3.
Therefore, the solution to the equation 3x + 5 = 14 is x = 3.
Question 2:
For this question, we are given the equation 2(4x – 5) = 26.
Step 1: Start by distributing the 2 to the terms inside the parentheses. This gives us 8x – 10 = 26.
Step 2: Next, add 10 to both sides of the equation to isolate the term with x. This gives us 8x = 26 + 10 = 36.
Step 3: Finally, divide both sides of the equation by 8 to solve for x. This gives us x = 36/8 = 4.5.
Therefore, the solution to the equation 2(4x – 5) = 26 is x = 4.5.
Check Your Work: Lesson 14 Homework 5.4 Answer Key
It is important to verify our answers to ensure accuracy. Let’s check the solutions we obtained for Question 1 and Question 2.
For Question 1, we can substitute the value of x = 3 back into the original equation 3x + 5 = 14. This gives us 3(3) + 5 = 14, which simplifies to 9 + 5 = 14. Since 9 + 5 = 14 is true, we can conclude that x = 3 is indeed the correct solution.
For Question 2, substituting x = 4.5 back into the original equation 2(4x – 5) = 26 gives us 2(4(4.5) – 5) = 26. Simplifying this further, we get 2(18 – 5) = 26, which becomes 2(13) = 26. Since 2(13) = 26 is true, we can confirm that x = 4.5 is the correct solution.
By following the step-by-step solutions provided in this answer key, you can now check your work for Lesson 14 Homework 5.4. Remember to always verify your answers to ensure accuracy. Understanding these concepts is crucial as they lay the foundation for more advanced topics. Keep practicing and you will continue to improve your skills in solving equations. Good luck!
