Wir müssen das größte \( k \) finden, sodass \( 7k + 3 \leq 100 \):

["Title: How to Solve ( 7k + 3 \leq 100 ): Find the Largest Integer ( k )", "In this SEO-optimized guide, we’ll walk you through the simple process of solving the inequality ( 7k + 3 \leq 100 ) to find the largest possible integer value of ( k ). This practical example is commonly encountered in algebra and math education, making it a great target for Search Engine optimization around math problem-solving, integer inequalities, and step-by-step algebraic reasoning.", "---", "### Understanding the Inequality", "We begin with the inequality:\n[\n7k + 3 \leq 100\n]", "This equation describes a linear relationship between ( k ) and a constant value. Our goal is to isolate ( k ) and determine the largest integer that satisfies this condition.", "---", "### Step-by-Step Solution", "1. Subtract 3 from both sides\n To isolate the term with ( k ), subtract 3 from both sides:\n [\n 7k \leq 100 - 3\n ]\n [\n 7k \leq 97\n ]", "2. Divide by 7\n Next, divide both sides by 7 to solve for ( k ):\n [\n k \leq \frac{97}{7}\n ]", "3. Simplify the fraction\n Perform the division:\n [\n \frac{97}{7} = 13.857\overline{142857}\n ]", "Since ( k ) must be an integer, we consider the greatest whole number less than or equal to 13.857…", "4. Determine the largest integer ( k )\n The largest integer satisfying ( k \leq 13.857 ) is ( k = 13 ).", "---", "### Final Answer", "[\n\boxed{k = 13}\n]", "---", "### Practical Implications and Key Takeaways", "Understanding how to solve inequalities like ( 7k + 3 \leq 100 ) is essential in everyday math practice. Such problems reinforce critical skills in algebra—solving for variables, manipulating expressions, and interpreting bounds.", "This type of question is often found in math curricula, standardized tests, and competitive exams, making mastery of inequality solving a valuable asset.", "Keywords for SEO optimization:\n- Solve ( 7k + 3 \leq 100\n- Find largest integer ( k ) satisfying inequality\n- Linear inequality algebra step-by-step\n- How to solve ( 7k + C \leq D\n- Integer solutions inequality", "---", "### Related Topics You May Explore\n- Solving linear equations with integers\n- Applications of inequalities in real life\n- Step-by-step algebra for beginners\n- How to isolate variables in inequalities", "---", "Give your math skills a strong foundation by mastering inequality solving — solving for ( k ) in ( 7k + 3 \leq 100 ) is a perfect starting point!"]