Simplify: \( 2y + 4 + y = 10 \) → \( 3y = 6 \) → \( y = 2 \)

Simplify: \( 2y + 4 + y = 10 \) → \( 3y = 6 \) → \( y = 2 \)

["How to Solve the Equation: ( 2y + 4 + y = 10 ) | Step-by-Step Simplification", "Solving simple linear equations is a fundamental skill in algebra, and mastering it helps build a strong math foundation. In this article, we’ll walk through the step-by-step process of solving the equation:", "[ 2y + 4 + y = 10 ]", "to find the value of ( y ), simplifying it clearly and logically—arriving at ( y = 2 ).", "---", "### Step 1: Combine Like Terms\nStart by simplifying the left-hand side of the equation. Both ( 2y ) and ( y ) are like terms that include the variable ( y ).", "[ 2y + y + 4 = 10 ]\n[ (2y + y) + 4 = 10 ]\n[ 3y + 4 = 10 ]", "Now the equation is simplified to:\n[ 3y + 4 = 10 ]", "---", "### Step 2: Isolate the Variable Term\nTo find ( y ), you need to eliminate the constant term ( +4 ) from the left side. Subtract 4 from both sides of the equation:", "[ 3y + 4 - 4 = 10 - 4 ]\n[ 3y = 6 ]", "Now you’re left with:\n[ 3y = 6 ]", "---", "### Step 3: Solve for ( y )\nSince ( y ) is multiplied by 3, divide both sides by 3 to isolate ( y ):", "[ \frac{3y}{3} = \frac{6}{3} ]\n[ y = 2 ]", "---", "### Final Answer\nThe solution to the equation ( 2y + 4 + y = 10 ) is:\n[ \boxed{y = 2} ]", "---", "Why This Step-by-Step Works\nBreaking equations into smaller steps ensures clarity and reduces mistakes. Combining like terms simplifies expressions, subtracting constants isolates variables, and dividing isolates the unknown. This method applies to many similar linear equations and prepares you for more complex algebraic problems.", "---", "### Pro Tips for Easy Equation Solving\n- Always combine like terms first.\n- Keep both sides of the equation balanced by performing the same operation on both.\n- Use inverse operations to isolate the variable.\n- Double-check your answer by substituting ( y = 2 ) back into the original equation.", "Try this process with other simple equations—you’ll master solving linear equations quickly!", "---", "Key Takeaways:\n- Combine like terms in ( 2y + y ) → ( 3y )\n- Move constants by subtraction: ( 3y + 4 = 10 → 3y = 6 )\n- Solve for ( y ) by dividing both sides by 3 → ( y = 2 )", "Understanding these steps helps unlock algebra and builds confidence in math!", "(Keywords: solve linear equation, simplify ( 2y + 4 + y = 10 ), step-by-step algebra, how to find y)"]

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2A^2 + 6Ad + 9d^2 = 16A^2 + 48Ad + 36d^2\Rightarrow 0 = 14A^2 + 42Ad + 27d^2.Divide by $ d^2 $: let $ x = \frac{A}{d} $, then:14x^2 + 42x + 27 = 0.Discriminant: $ 42^2 - 4\cdot14\cdot27 = 1764 - 1512 = 252 = 36 \cdot 7 $.x = \frac{-42 \pm 6\sqrt{7}}{28} = \frac{-21 \pm 3\sqrt{7}}{14}.Third term: $ A + 2d $, first: $ A $, so ratio:\frac{A + 2d}{A} = 1 + 2\frac{d}{A} = 1 + 2\frac{1}{x} = 1 + \frac{2x}{-21 \pm 3\sqrt{7}}.Take positive root for real chance (positive terms): $ x = \frac{-21 + 3\sqrt{7}}{14} $. Compute numerically: $ \sqrt{7} \approx 2.6458 $, $ 3\sqrt{7} \approx 7.937 $, so $ x \approx \frac{-21 + 7.937}{14} = \frac{-13.063}{14} \approx -0.932 $. Then $ \frac{1}{x} \approx -1.073 $, so $ 1 + 2(-1.073) = -1.146 $. Not meaningful.But from quadratic: $ 14x^2 + 42x + 27 = 0 $. Product of roots $ \frac{27}{14} $, sum $ -3 $.