Simplify to \(8w = 64\), so \(w = 8\).

["# Simplify to (8w = 64), Then Find (w = 8): A Clear Guide to Solving Linear Equations", "Understanding how to solve simple linear equations is a fundamental skill in algebra—and mastering it helps build confidence for more complex math problems. In this article, we’ll break down one of the most straightforward equation solving processes: simplifying (8w = 64) and finding that (w = 8). Whether you're a student learning algebra or helping someone else, this step-by-step guide will simplify the process.", "## What Is the Equation (8w = 64)?", "At its core, the equation (8w = 64) means that eight times an unknown number (w) equals sixty-four. This is a linear equation because it involves a variable multiplied by a constant—key signs that it belongs to the basic category of linear equations.", "## Step-by-Step Simplification", "### Step 1: Isolate the Variable", "To solve for (w), we need to isolate it on one side of the equation. Since (w) is being multiplied by 8, we reverse this operation by dividing both sides by 8:", "[\n8w = 64\n]", "Divide both sides by 8:\n[\nw = \frac{64}{8}\n]", "### Step 2: Perform the Division", "Now compute:", "[\n\frac{64}{8} = 8\n]", "Thus,", "[\nw = 8\n]", "---", "## Why This Method Works", "The key principle behind solving (8w = 64) is the inverse operation. Multiplication by 8 can be undone exactly by dividing by 8. This maintains equation balance—what you do to one side, you must do to the other.", "---", "## How to Apply This Logic in Real-World Problems", "Knowing how to solve (8w = 64) prepares you to tackle similar equations, such as:", "- (3w = 27) → (w = 9)\n- (5w = 45) → (w = 9)\n- (10w = 100) → (w = 10)", "These are commonly used in practical scenarios such as calculating unit prices, scaling recipes, or determining time and distance when rates are known.", "---", "## Summary", "- The equation (8w = 64) simplifies to finding the value of (w) that makes 8 times it equal 64.\n- Dividing both sides by 8 yields (w = 8).\n- This teaches a core algebraic skill: isolating variables using inverse operations.\n- Mastering such equations is foundational for all algebra learners.", "---", "## Additional Tips for Students and Learners", "- Check your answer: Plug (w = 8) back into the original equation:\n (8(8) = 64) → (64 = 64), which checks!\n- Practice with different coefficients to build fluency.\n- Use balancing act visualization—always keep the equation equal on both sides.\n- Use algebra tiles or drawing models to see how multiplication and division interact visually.", "---", "By simplifying (8w = 64) to (w = 8), you not only solve one equation—you reinforce a vital strategy for success in algebra and beyond. Keep practicing, and algebra will become second nature!"]