\cdot \frac{122}{19} + 3b = 43 \Rightarrow \frac{610}{19} + 3b = 43 \Rightarrow 3b = 43 - \frac{610}{19} = \frac{817 - 610}{19} = \frac{207}{19}

["Solving the Equation: $\frac{122}{19} + 3b = 43$ Step-by-Step", "Understanding how to solve linear equations is essential in algebra, and mastering step-by-step problem-solving makes complex expressions manageable. In this article, we’ll walk through solving the equation:", "$$\n\frac{122}{19} + 3b = 43\n$$", "and derive the solution showing intermediate steps, so you can clearly see how to simplify expressions like $\frac{122}{19} + 3b$ and isolate the variable $b$.", "---", "### Step 1: Move the Constant Fraction to the Right Side\nWe begin by isolating the term with the variable $b$. Subtract $\frac{122}{19}$ from both sides:", "$$\n3b = 43 - \frac{122}{19}\n$$", "---", "### Step 2: Convert Whole Number to a Fraction with Common Denominator\nTo simplify the subtraction, convert $43$ into a fraction with denominator 19:", "$$\n43 = \frac{43 \ imes 19}{19} = \frac{817}{19}\n$$", "So the equation becomes:", "$$\n3b = \frac{817}{19} - \frac{122}{19}\n$$", "---", "### Step 3: Subtract the Fractions\nSince both fractions share the same denominator, subtract the numerators:", "$$\n3b = \frac{817 - 122}{19} = \frac{695}{19}\n$$", "Wait — here’s a correction from your original derivation:\nEarlier you stated:\n$$\n43 - \frac{610}{19} = \frac{207}{19}\n$$\nBut actually, the correct numerator is $817 - 122 = 695$, so:", "$$\n3b = \frac{695}{19}\n$$", "---", "### Step 4: Solve for $b$\nNow divide both sides by 3 to isolate $b$:", "$$\nb = \frac{695}{19} \div 3 = \frac{695}{19 \ imes 3} = \frac{695}{57}\n$$", "---", "### Step 5: Simplify (If Possible)\nCheck if $\frac{695}{57}$ reduces:\n$\gcd(695, 57) = 1$, so the fraction is already in simplest form.", "---", "### Final Answer\n$$\nb = \frac{695}{57}\n$$", "---", "### Summary\nThe key steps in solving $\frac{122}{19} + 3b = 43$ are:\n- Isolate $3b$ by subtracting the constant fraction\n- Convert whole numbers to fractions with common denominators\n- Perform precise arithmetic on numerators\n- Divide by 3 to solve for $b$", "Understanding these steps helps build confidence in manipulating expressions like $\frac{122}{19} + 3b$. For example, converting $43$ to a fraction with denominator 19 is crucial—it transforms subtraction into a clean numerical operation.", "If you’re working on similar equations such as $\frac{610}{19} + 3b = 43$, follow the same logic—just replace numerators accordingly to simplify.", "---", "Key Takeaways:\n- Always convert whole numbers to fractions when subtracting from others\n- Keep denominators consistent for smooth arithmetic\n- Isolate the variable before solving\n- Simplify fractions when possible to express final answers clearly", "Mastering these algebra fundamentals unlocks stronger problem-solving skills in math and related STEM fields.", "---", "Related Topics:\n- Solving linear equations with fractions\n- Simplifying algebraic expressions involving constants\n- Divide both sides: when isolating variables\n- Understanding LCM in fraction subtraction", "---", "Keywords for SEO: solve linear equation, fraction arithmetic, algebra step-by-step, simplify $\frac{122}{19} + 3b$, equation solving tutorial, how to solve for $b$, combine constants and variables, algebra step-by-step guide, simplify rational expressions, linear equation solver, fraction subtraction in algebra."]