Substitute into (B): \( 5a + (2.5 - a) = 1.5 \Rightarrow 4a + 2.5 = 1.5 \Rightarrow 4a = -1 \Rightarrow a = -\frac{1}{4} \)

["# Solving the Equation: How to Solve ( 5a + (2.5 - a) = 1.5 ) Step-by-Step", "Solving linear equations is a fundamental skill in algebra, and understanding the step-by-step process builds confidence and accuracy. One common algebraic equation students encounter is:", "[\n5a + (2.5 - a) = 1.5\n]", "This equation might appear simple, but mastering its solution involves recognizing parentheses, combining like terms, and isolating the variable — all critical steps for algebraic proficiency. In this article, we’ll break down how to solve this equation and verify the solution clearly, helping you apply the method to similar problems.", "---", "### Step 1: Simplify the Left Side", "Start by eliminating the parentheses. In this case, the expression ( 2.5 - a ) is added to ( 5a ), so combine ( 5a ) and ( -a ):", "[\n5a - a + 2.5 = 1.5\n]", "This simplifies to:", "[\n4a + 2.5 = 1.5\n]", "By combining like terms, we reduced the equation to a simpler linear form.", "---", "### Step 2: Isolate the Variable Term", "Next, subtract ( 2.5 ) from both sides to isolate the term with the variable ( a ):", "[\n4a + 2.5 - 2.5 = 1.5 - 2.5\n]", "Which simplifies to:", "[\n4a = -1\n]", "This step demonstrates the fundamental principle of balancing equations: subtracting the same value from both sides preserves equality.", "---", "### Step 3: Solve for ( a )", "Now divide both sides by 4 to solve for ( a ):", "[\na = \frac{-1}{4}\n]", "Or as a decimal:", "[\na = -0.25\n]", "---", "### Why Understanding This Matters", "Solving equations like ( 5a + (2.5 - a) = 1.5 ) teaches key algebraic strategies:", "- How to expand and simplify expressions using parentheses\n- Practice combining like terms\n- The importance of isolating variables\n- Stepwise simplification to reveal solutions", "This foundational method applies directly to more complex equations in algebra, physics, economics, and engineering contexts.", "---", "### Final Answer", "[\na = -\frac{1}{4}\n]", "---", "By mastering this equation and similar linear problems, you lay the groundwork for advanced math success. Always remember: patience, clarity, and careful step-by-step execution are your greatest tools in solving equations. Whether you're a student or looking to brush up, understanding how to solve such equations empowers accurate problem-solving across disciplines.", "---", "Keywords: solve linear equations, algebra step-by-step, equation solving tutorial, substitution method, linear equation solution, algebra basics, step-by-step math, solve for a, rational numbers in equations.", "Meta Description: Learn how to solve ( 5a + (2.5 - a) = 1.5 ) step-by-step, including simplifying expressions, combining like terms, and isolating the variable. Find clear explanations and practice solutions to master algebra."]