2\left(\frac{43 - 3b}{5}\right) + 5b = 31 \Rightarrow \frac{86 - 6b}{5} + 5b = 31

["Solve 2\left(\frac{43 - 3b}{5}\right) + 5b = 31: Step-by-Step Breakthrough", "Understanding how to solve equations like 2\left(\frac{43 - 3b}{5}\right) + 5b = 31 is essential for mastering algebra. This step-by-step guide breaks down the process clearly, helping students and math learners alike solve this type of linear equation efficiently.", "---", "### The Original Equation", "Start with:", "$$\n2\left(\frac{43 - 3b}{5}\right) + 5b = 31\n$$", "---", "### Step 1: Clear the fraction", "Multiply both sides of the equation by 5 to eliminate the denominator:", "$$\n5 \cdot \left[ 2\left(\frac{43 - 3b}{5}\right) + 5b \right] = 5 \cdot 31\n$$", "Simplify both sides:", "$$\n2(43 - 3b) + 25b = 155\n$$", "---", "### Step 2: Expand the expression", "Distribute the 2:", "$$\n86 - 6b + 25b = 155\n$$", "Combine like terms:", "$$\n86 + 19b = 155\n$$", "---", "### Step 3: Isolate the variable term", "Subtract 86 from both sides:", "$$\n19b = 155 - 86\n$$", "$$\n19b = 69\n$$", "---", "### Step 4: Solve for ( b )", "Divide both sides by 19:", "$$\nb = \frac{69}{19}\n$$", "---", "### Verifying the solution", "Plug ( b = \frac{69}{19} ) back into the original equation:", "$$\n2\left(\frac{43 - 3\cdot\frac{69}{19}}{5}\right) + 5 \cdot \frac{69}{19} = 31\n$$", "Compute step-by-step:", "- ( 3 \cdot \frac{69}{19} = \frac{207}{19} )\n- ( 43 - \frac{207}{19} = \frac{817 - 207}{19} = \frac{610}{19} )\n- Divide by 5: ( \frac{610}{19 \cdot 5} = \frac{122}{19} )\n- Multiply by 2: ( 2 \cdot \frac{122}{19} = \frac{244}{19} )\n- ( 5 \cdot \frac{69}{19} = \frac{345}{19} )", "Add both parts:", "$$\n\frac{244 + 345}{19} = \frac{589}{19} = 31\n$$", "✔️ The solution checks out.", "---", "### Why This Matters (SEO Optimization)", "Understanding how to solve linear equations with fractions and parentheses is foundational in algebra. Mastering step-by-step techniques improves problem-solving speed and accuracy, essential for students preparing for standardized tests, or anyone looking to strengthen logical reasoning and mathematical fluency.", "### Key takeaways:", "- Multiply through by the denominator to eliminate fractions\n- Expand and combine like terms carefully\n- Isolate the variable and solve linearly\n- Verify the solution by substitution", "---", "Final Answer:", "$$\nb = \frac{69}{19}\n$$", "Use this technique to confidently solve similar equations and boost your algebra skills today!", "---", "Keywords: solve linear equation, algebra solving steps, simplify fractions, linear equation with variables, step-by-step algebra, solve 2(43−3b)/5 + 5b = 31, algebraic manipulation, how to solve equations, math tutorials, equation solving guide", "Meta Description:\nLearn how to solve the equation ( 2\left(\frac{43 - 3b}{5}\right) + 5b = 31 ) step-by-step. Step-by-step breakdown, verification, and key algebra tips make solving such equations easier."]