\[ 4 + 0,7x = 0,5(10 + x) \] - Verified Servers

["# Solving the Equation: 4 + 0,7x = 0,5(10 + x) — A Step-by-Step Guide", "Understanding how to solve linear equations is essential for mastering algebra and building strong problem-solving skills. One common equation students encounter is:", "4 + 0,7x = 0,5(10 + x)", "If you're struggling to solve this or want a clear, step-by-step explanation, you’re in the right place! In this article, we’ll break down how to solve this equation, explain the key algebraic concepts involved, and highlight its real-world applications.", "---", "## Why Solve Linear Equations Like This?", "Linear equations are foundational in mathematics, appearing in science, economics, engineering, and everyday decision-making. The equation 4 + 0,7x = 0,5(10 + x) may look simple, but solving it trains your ability to manipulate variables, distribute expressions, and isolate unknowns — skills critical for higher-level math and analytical thinking.", "---", "## Step-by-Step Solution", "### Step 1: Expand the right-hand side", "Start by simplifying the right side of the equation using the distributive property:
\n[ 0,5(10 + x) = 0,5 \cdot 10 + 0,5 \cdot x = 5 + 0,5x ]", "Now your equation becomes:
\n[ 4 + 0,7x = 5 + 0,5x ]", "### Step 2: Move all terms involving ( x ) to one side", "Subtract ( 0,5x ) from both sides to collect like terms:
\n[ 4 + 0,7x - 0,5x = 5 ]
\n[ 4 + 0,2x = 5 ]", "### Step 3: Isolate the ( x )-term", "Subtract 4 from both sides:
\n[ 0,2x = 5 - 4 ]
\n[ 0,2x = 1 ]", "### Step 4: Solve for ( x )", "Divide both sides by 0,2 (also write 0.2 as ( \frac{1}{5} )):
\n[ x = \frac{1}{0,2} = \frac{1}{\frac{1}{5}} = 5 ]", "---", "## Final Answer", "[
\n\boxed{x = 5}
\n]", "---", "## Verification", "Plug ( x = 5 ) back into the original equation to confirm:
\nLeft side: ( 4 + 0,7 \cdot 5 = 4 + 3,5 = 7,5 )
\nRight side: ( 0,5(10 + 5) = 0,5 \cdot 15 = 7,5 )
\nBoth sides equal 7.5, so the solution is correct.", "---", "## Real-World Application Example", "Imagine you’re managing a small business selling eco-friendly notebooks.
\n- Cost per notebook: $4
\n- You charge $0.7 more per notebook than the flat $5 guaranteed price point.
\n- For every notebook sold above base, your effective average price drops based on volume — modeled here as:
\n [ \ ext{Effective average price} = 4 + 0,7x ]
\n- Meanwhile, if you bundle materials costing $10 and each unit adds $0.5 overhead, your model becomes:
\n [ \ ext{Bundled cost} = 0,5(10 + x) ]", "The equation 4 + 0,7x = 0,5(10 + x) balances both pricing assumptions. Finding ( x = 5 ) means selling 5 notebooks adjusts the pricing model to break even or meet average cost targets.", "---", "## Conclusion", "Solving equations like 4 + 0,7x = 0,5(10 + x) strengthens algebraic fluency and problem-solving insight. By expanding, isolating variables, and verifying solutions, students gain confidence in tackling increasingly complex math challenges — skills that pave the way for success in STEM fields and beyond.", "💡 Pro Tip: Practice with different coefficients and constants to master pattern recognition and equation solving.", "---", "## Keywords for SEO Optimization
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\n- Solve 4 + 0.7x = 0.5(10 + x)
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\n- Solve for x with coefficients", "---", "Get practice solving linear equations today — master the basics, ace your math exams, and unlock advanced learning!"]