To solve the inequality \( 7x - 3 > 25 + 3x \), we will follow a step-by-step approach to isolate \( x \) and determine the range of values that satisfy the inequality. ### Step 1: Rearranging the Inequality We start with the original inequality: \[ 7x - 3 > 25 + 3x \] Our goal is to get all terms involving \( x \) on one side and constant terms on the other side. To do this, we can subtract \( 3x \) from both sides: \[ 7x - 3x - 3 > 25 \] This simplifies to: \[ 4x - 3 > 25 \] ### Step 2: Isolating \( x \) Next, we need to isolate \( 4x \). We can do this by adding \( 3 \) to both sides of the inequality: \[ 4x > 25 + 3 \] This simplifies to: \[ 4x > 28 \] Now, we divide both sides by \( 4 \) to solve for \( x \): \[ x > \frac{28}{4} \] Calculating the right side gives us: \[ x > 7 \] ### Conclusion The solution to the inequality \( 7x - 3 > 25 + 3x \) is: \[ x > 7 \] Thus, the correct option is **A. x > 7**. ### Explanation of Other Options Now, let's analyze the other options to understand why they are incorrect: - **B. x < 7**: This option suggests that \( x \) is less than \( 7 \). However, our solution indicates that \( x \) must be greater than \( 7 \). Therefore, this option is incorrect. - **C. x > -7**: This option states that \( x \) is greater than \( -7 \). While this is true for many values of \( x \), it does not satisfy the specific condition we derived from the inequality, which requires \( x \) to be greater than \( 7 \). Thus, this option is too broad and incorrect. - **D. x < -7**: This option suggests that \( x \) is less than \( -7 \). This is not consistent with our solution, which requires \( x \) to be greater than \( 7 \). Therefore, this option is also incorrect. ### Summary of Key Points - To solve the inequality \( 7x - 3 > 25 + 3x \), we rearranged the terms to isolate \( x \). - We simplified the inequality step-by-step, leading to the conclusion that \( x > 7 \). - The correct answer is **A. x > 7**. - The other options are incorrect because they do not satisfy the derived condition from the inequality. ### Revision Summary - Rearrange the inequality to isolate \( x \). - Perform operations carefully to maintain the inequality's direction. - Check each option against the derived solution to confirm correctness. - Remember that inequalities can have strict (>) or non-strict (≥) conditions, affecting the solution set.