Simplify: \( 2x + 12x - 27 = 16 \).

["Simplify ( 2x + 12x - 27 = 16 ): Step-by-Step Guide", "Solving linear equations like ( 2x + 12x - 27 = 16 ) might seem tricky at first, but with a clear step-by-step approach, you can simplify and solve it easily. This article breaks down how to simplify and solve the equation to find the value of ( x ), making algebraic problem-solving simple and intuitive.", "---", "### Understanding the Equation", "Begin with the equation:", "[\n2x + 12x - 27 = 16\n]", "This equation combines like terms—specifically, the terms with ( x ). Let's simplify it first.", "---", "### Step 1: Combine Like Terms", "The terms ( 2x ) and ( 12x ) are like terms because they both contain ( x ). Add them together:", "[\n2x + 12x = 14x\n]", "Now, rewrite the equation:", "[\n14x - 27 = 16\n]", "---", "### Step 2: Isolate the Variable Term", "To simplify further, eliminate the constant term on the left. Add 27 to both sides of the equation:", "[\n14x - 27 + 27 = 16 + 27\n]", "[\n14x = 43\n]", "---", "### Step 3: Solve for ( x )", "Now, divide both sides by 14 to solve for ( x ):", "[\nx = \frac{43}{14}\n]", "---", "### Final Answer", "[\n\boxed{x = \frac{43}{14}}\n]", "---", "### Summary", "Simplifying ( 2x + 12x - 27 = 16 ) involves combining like terms, isolating the variable, and solving linearly. Following these straightforward steps ensures accurate and quick solutions for similar linear equations.", "Whether you’re a student mastering algebra or looking to refresh your algebra skills, simplifying such equations builds a strong foundation in mathematical problem-solving. Use this step-by-step method anytime you encounter ( ax + b = c )—you’ll find simplifying linear equations easier than ever!", "---", "Keywords: Simplify (2x + 12x - 27 = 16), linear equation, step-by-step solution, algebra, solving equations, math help, simplify algebraic expressions."]