ight) + p = 6 \Rightarrow rac{14}{3} + p = 6 \Rightarrow p = 6 - rac{14}{3} = rac{18 - 14}{3} = rac{4}{3}

["Understanding Algebraic Equations: How to Solve for a Variable Step-by-Step", "Learning algebra is a fundamental step toward mastering mathematics. One common type of problem students encounter involves solving equations with variables on both sides, like ( i + p = 6 ), where ( i ) and ( p ) are unknown values. In this article, we’ll explore how to solve the equation ( i + p = 6 ) when ( p = 6 - \frac{14}{3} ) — and how such expressions simplify using algebraic principles.", "---", "### The Original Equation", "Start with the equation:\n[ i + p = 6 ]", "We’re told that:\n[ p = 6 - \frac{14}{3} ]", "---", "### Step 1: Substitute the Given Value of ( p )", "Replace ( p ) in the original equation:\n[ i + \left(6 - \frac{14}{3}\right) = 6 ]", "Now solve for ( i ):\n[ i = 6 - \left(6 - \frac{14}{3}\right) ]\n[ i = 6 - 6 + \frac{14}{3} ]\n[ i = \frac{14}{3} ]", "---", "### Step 2: Simplify Using Algebraic Rules", "The simplification relies on the property of equality: subtracting a value from both sides. However, the key insight lies in recognizing how subtraction interacts with negative terms. When you write:\n[ i = 6 - \left(6 - \frac{14}{3}\right) ]\nthis is equivalent to:\n[ i = (6 - 6) + \frac{14}{3} = 0 + \frac{14}{3} = \frac{14}{3} ]", "On the other hand, if you interpret:\n[ i + p = 6 \Rightarrow i = 6 - p ]\nand plug in ( p = 6 - \frac{14}{3} ), then:\n[ i = 6 - \left(6 - \frac{14}{3}\right) = \frac{14}{3} ]", "Both approaches confirm that ( i = \frac{14}{3} ), showing how substitution and the distributive principle streamline solving equations.", "---", "### Why Is This Important?", "Understanding how to manipulate expressions like ( 6 - \frac{14}{3} ) and solve for other variables builds strong algebraic fluency. This foundational skill supports more complex equations in math, science, engineering, and programming.", "---", "### Final Answer", "[ i = \frac{14}{3} ]\nExpressed as a combined fraction:\n[ 6 - \frac{14}{3} = \frac{18}{3} - \frac{14}{3} = \frac{4}{3} ]\nbut in this context:\n[ i = \frac{14}{3} \quad \ ext{and} \quad p = 6 - \frac{14}{3} = \frac{4}{3} ]", "---", "### Summary", "- Substitute known values into equations carefully.\n- Use algebraic properties like subtraction and distribution to simplify expressions.\n- Solve step-by-step to arrive at accurate solutions.\n- Mastering these algebraic techniques is key to progressing in STEM fields.", "If you're learning algebra, practice replacing variables and simplifying expressions — soon you’ll solve complex equations with confidence!", "---", "Keywords: algebraic equation solving, solve for variable, linear equation, algebra tutorial, simplify fractions, solve ( i + p = 6 ), step-by-step algebra, subtracting mixed numbers in algebra, equation substitution, math basics for students.", "Meta Title: Solve ( i + p = 6 ) with ( p = 6 - \frac{14}{3} ): Step-by-step algebraic solution", "Meta Description: Learn how to solve algebraic equations like ( i + p = 6 ) when one variable equals ( 6 - \frac{14}{3} ). Step-by-step breakdown shows substitution and simplification."]