Simplify: \(86/14 + 3y = 16\), or \(3y = 16 - 43/7\).
["How to Simplify the Equation: ( \frac{86}{14} + 3y = 16 )", "Solving linear equations step by step can sometimes feel overwhelming, but simplifying equations like ( \frac{86}{14} + 3y = 16 ) becomes much easier with a clear approach. In this article, we’ll break down how to simplify this equation and solve for ( y ), including simplifying the right-hand side expression ( 16 - \frac{43}{7} ) correctly.", "---", "### Understanding the Equation\nStart with the equation:\n[ \frac{86}{14} + 3y = 16 ]", "First, simplify the fraction ( \frac{86}{14} ).\nSimplify by dividing numerator and denominator by 2:\n[ \frac{86 \div 2}{14 \div 2} = \frac{43}{7} ]", "So the equation now is:\n[ \frac{43}{7} + 3y = 16 ]", "---", "### Rewrite for Simpler Solving\nTo isolate ( 3y ), subtract ( \frac{43}{7} ) from both sides:\n[ 3y = 16 - \frac{43}{7} ]", "Now simplify the right-hand side expression ( 16 - \frac{43}{7} ).", "Note that 16 can be written as a fraction with denominator 7:\n[ 16 = \frac{16 \ imes 7}{7} = \frac{112}{7} ]", "So,\n[ 3y = \frac{112}{7} - \frac{43}{7} = \frac{112 - 43}{7} = \frac{69}{7} ]", "---", "### Solve for ( y )\nNow divide both sides by 3:\n[ y = \frac{69}{7} \div 3 = \frac{69}{7} \ imes \frac{1}{3} = \frac{69}{21} ]", "Simplify ( \frac{69}{21} ): both numerator and denominator are divisible by 3:\n[ \frac{69 \div 3}{21 \div 3} = \frac{23}{7} ]", "---", "### Final Answer\n[ y = \frac{23}{7} \quad \ ext{or approximately} \quad y \approx 3.29 ]", "---", "### Why This Step-by-Step Matters\nSimplifying fractions and properly handling arithmetic expressions like ( 16 - \frac{43}{7} ) ensures accuracy and clarity in solving equations. Expressions like ( 3y = \frac{69}{7} ) allow direct, straightforward computation to isolate ( y ). Understanding each step makes solving similar linear equations much more manageable.", "If you're working on linear equations in algebra, remember: simplify fractions first, combine like terms carefully, and always convert to common denominators when subtracting mixed numbers or integers.", "---", "Keywords: simplify equation, solve linear equation, simplify 86/14, simplify 3y = 16 - 43/7, step-by-step math, algebra tutorial, how to solve variables"]
