Subtract 7 from both sides: \( 3x = 15 \)
["How to Solve the Equation: Subtract 7 from Both Sides of ( 3x = 15 )", "When solving linear equations, one of the most common and effective steps is eliminating constants by performing the same operation on both sides. In the equation ( 3x = 15 ), a foundational step is subtracting 7 from both sides. While this might seem simple, it plays a crucial role in isolating the variable and simplifying the equation for further solving.", "### Understanding the Equation: ( 3x = 15 )", "At first glance, ( 3x = 15 ) means that three times some unknown value ( x ) equals 15. To find ( x ), we need to isolate it. Since 15 is accompanied only by a constant, subtracting 7 from both sides helps reduce the equation’s complexity.", "### Why Subtract 7 from Both Sides?", "Subtracting 7 from both sides maintains the equality while simplifying the right-hand side:", "[\n3x - 7 = 15 - 7\n]", "[\n3x - 7 = 8\n]", "This step removes the constant on the right-hand side, bringing us closer to isolating ( x ). While subtracting 7 alone doesn’t fully isolate ( x ) (since ( x ) is multiplied by 3), it sets the stage for the final solution.", "### Moving Forward: Solve for ( x )", "Now we solve:", "[\n3x = 15 - 7\n]", "[\n3x = 8\n]", "Next, divide both sides by 3:", "[\nx = \frac{8}{3}\n]", "Thus, solving ( 3x = 15 ) after subtracting 7 from both sides leads to ( x = \frac{8}{3} ), or approximately 2.67.", "### Why This Step Matters: A Key Algebraic Strategy", "Subtracting 7 from both sides of ( 3x = 15 ) teaches a vital algebra principle: performing the same operation on both sides preserves equality. This approach is foundational for solving more complex equations and builds a strong base for topics like systems of equations and solving for variables in real-world problems.", "### Applying the Concept in Real Life", "This type of equation solving is not only academic—it’s practical. Whether balancing budgets, analyzing data, or designing engineering models, isolating variables efficiently using equivalent operations ensures accurate and reliable results.", "### Final Thoughts", "Subtracting 7 from both sides of ( 3x = 15 ) is a simple yet powerful step in the journey of solving linear equations. It exemplifies how a small adjustment can transform an equation into a manageable form, reinforcing clear reasoning and precise computation. By mastering this technique, students and learners build confidence in algebra and equip themselves for success in advanced math and STEM fields."]
