\[ 4x + 6 = -x + 2 \] - Project Allmight

["Solving the Equation 4x + 6 = -x + 2: A Step-by-Step Guide", "Understanding how to solve linear equations is a fundamental skill in algebra and essential for anyone studying math, science, or related fields. One of the most common types of problems students encounter is solving equations like 4x + 6 = -x + 2. This article provides a clear, detailed step-by-step solution to help you master this process.", "---", "### What is the Equation?", "The equation we are solving is:
\n[
\n4x + 6 = -x + 2
\n]", "Our goal is to isolate the variable x on one side of the equation to find its value.", "---", "### Step 1: Eliminate Variables on One Side", "We begin by moving all terms containing x to the left side and constant terms to the right side.", "- Start by adding x to both sides to eliminate -x on the right:", "[
\n4x + x + 6 = -x + x + 2
\n]
\n[
\n5x + 6 = 2
\n]", "- Next, subtract 6 from both sides to isolate the term with x:", "[
\n5x + 6 - 6 = 2 - 6
\n]
\n[
\n5x = -4
\n]", "---", "### Step 2: Solve for x", "Now divide both sides by 5 to solve for x:", "[
\nx = \frac{-4}{5}
\n]", "---", "### Final Answer", "The solution to the equation 4x + 6 = -x + 2 is:
\n[
\nx = -\frac{4}{5}
\n]", "---", "### Why This Equation Matters", "This type of equation forms the basis for more complex algebraic manipulations used in solving inequalities, systems of equations, and real-world applications such as budgeting, physics, and engineering. Mastering these steps helps build strong problem-solving skills.", "---", "### Tips for Solving Similar Equations", "- Always perform the same operation on both sides of the equation to maintain balance.
\n- Combine like terms carefully before isolating variables.
\n- Check your solution by substituting x = -4/5 back into the original equation.", "---", "### Verification (Check Your Work)", "Substitute x = -4/5 into the original:
\nLeft side:
\n[
\n4\left(-\frac{4}{5}\right) + 6 = -\frac{16}{5} + \frac{30}{5} = \frac{14}{5}
\n]
\nRight side:
\n[
\n-\left(-\frac{4}{5}\right) + 2 = \frac{4}{5} + \frac{10}{5} = \frac{14}{5}
\n]
\nBoth sides equal 14/5, confirming the solution is correct.", "---", "Mastering linear equations starts here—keep practicing, and you’ll gain confidence quickly!", "---", "Keywords:
\n4x + 6 = -x + 2, solve linear equations, algebra step-by-step, equation solving tutorial, linear equation solutions, algebra homework help, intermediate algebra, solving for x, algebra explained, math problems, grade 8 algebra, math tips", "Meta Description:
\nLearn how to solve the equation 4x + 6 = -x + 2 step-by-step. Find clear explanations, detailed solution, and tips to master algebra fundamentals. Ideal for students and educators.", "---", "If you want more algebra help, explore related topics like quadratic equations, graphing linear inequalities, or system of equations for deeper understanding. Start today and unlock your math potential!"]