\[ 2(3w) = 60 \] - United Radiology

["Solving ( 2(3w) = 60 ) – A Step-by-Step Guide for Beginners", "Understanding how to solve algebraic equations is a fundamental skill that empowers students and lifelong learners alike. One common equation that often appears in basic math problems is ( 2(3w) = 60 ). Whether you're a student tackling homework, a teacher preparing lessons, or someone brushing up on algebra, solving this equation step-by-step can improve your mathematical confidence.", "### What Does the Equation Mean?", "The expression ( 2(3w) = 60 ) combines multiplication and variables. Here, ( w ) represents an unknown value, and the equation states that twice the product of ( 3 ) and ( w ) equals 60. Solving it involves isolating ( w ) to find its numerical value.", "### How to Solve ( 2(3w) = 60 )", "Let’s solve the equation step-by-step using elementary algebra:", "1. Simplify the left-hand side
\n Since 2 and 3 multiply together inside the parentheses, multiply them first:
\n [
\n 2(3w) = 6w
\n ]
\n So the equation becomes:
\n [
\n 6w = 60
\n ]", "2. Isolate the variable ( w )
\n To find ( w ), divide both sides of the equation by 6:
\n [
\n w = \frac{60}{6} = 10
\n ]", "### Final Answer
\n[
\nw = 10
\n]", "### Why Understanding This Equation Matters", "- Foundation for Algebra: Mastering simple linear equations builds a strong base for more complex math.
\n- Real-World Applications: Similar equations model real-life scenarios like calculating prices, proportions, and rates.
\n- Improves Problem-Solving Skills: Learning to isolate variables strengthens logical thinking and analytical reasoning.", "### Tips for Solving Similar Equations", "- Always simplify expressions inside parentheses first.
\n- Use inverse operations (division/division, addition/subtraction) to isolate the variable.
\n- Double-check your solution by substituting back into the original equation.", "Example verification:
\nPlugging ( w = 10 ) into ( 2(3w) ):
\n[
\n2(3 \ imes 10) = 2(30) = 60 \quad \ ext{✓ Correct!}
\n]", "### Summary", "Solving ( 2(3w) = 60 ) is a straightforward but valuable exercise in algebra. By simplifying step-by-step and carefully applying inverse operations, you find that ( w = 10 ). This moment of clarity not only answers the equation but also deepens your mathematical toolkit for future challenges.", "Whether studying at home, in class, or online, mastering equations like this one is key to success—keep practicing, stay curious, and let algebra build your confidence!", "---", "Keywords: solve ( 2(3w) = 60 ), algebra tutorial, equation solving steps, linear equations for beginners, how to solve 6w = 60, math help for students."]