["# Solving Linear Equations: Subtracting 3 from Both Sides in (3x = 69)", "Solving linear equations is a foundational skill in algebra, and one essential technique is manipulating equations by performing the same operation on both sides. A common operation is subtracting a constant from both sides—this helps isolate the variable and simplify the equation. This article explores how subtracting 3 from both sides transforms the equation (3x = 69), making it easier to solve for (x).", "## Why Subtract 3 from Both Sides?", "When solving equations, your goal is to isolate the variable—here, (x). In (3x = 69), (x) is multiplied by 3, so subtraction is used to eliminate that constant term. But why do we subtract 3 specifically?", "Because (3x) means (x) added three times, removing 3 from the right-hand side balances the equation. Subtracting 3 on both sides preserves the equality while reducing the equation to a simpler form:
\n[ 3x - 3 = 69 - 3 ]
\n[ 3x - 3 = 66 ]", "---", "## Step-by-Step: Subtract 3 from Both Sides", "Start with the original equation:
\n[ 3x = 69 ]", "Step 1: Subtract 3 from both sides:
\n[ 3x - 3 = 69 - 3 ]", "Step 2: Simplify both sides:
\n[ 3x - 3 = 66 ]", "Now, you can proceed by adding 3 back to isolate (3x) before dividing:
\n[ 3x = 66 ]
\nThen divide both sides by 3 to find (x):
\n[ x = \frac{66}{3} = 22 ]", "---", "## Final Answer", "After subtracting 3 from both sides of (3x = 69), simplifying yields:
\n[ x = 22 ]", "---", "## Tips for Mastering Subtraction in Equation Solving", "- Always perform the same operation on both sides to maintain equality.
\n- Simplify left and right carefully to avoid errors.
\n- Use inverse operations strategically—subtracting 3 leads to adding 3 afterward.
\n- Check your solution by substituting (x = 22) back into the original equation.", "---", "## Summary", "Subtracting 3 from both sides of (3x = 69) is a straightforward yet powerful step in solving linear equations. It models the principle of balance: subtracting the same value maintains equality while helping isolate the variable. With practice, manipulating equations this way becomes quick and intuitive—essential for math success!", "---", "Looking to strengthen your algebra skills? Learning to subtract constants in equations is a key step toward mastering linear equations and beyond. Keep practicing—each problem builds your confidence and precision!"]
