Expand: \( 20x + 5250 - 35x = 4000 \).

["# Expand and Solve: How to Solve ( 20x + 5250 - 35x = 4000 )", "If you’re tackling algebra problems like ( 20x + 5250 - 35x = 4000 ), expanding and solving it step-by-step is essential. Not only does this help in finding the value of ( x ), but it also strengthens your foundational math skills for more complex equations. In this article, we’ll guide you through expanding, simplifying, and solving this linear equation clearly and effectively.", "## Understanding the Equation", "We start with the equation:\n[\n20x + 5250 - 35x = 4000\n]", "At first glance, the equation involves variables and constants combined with arithmetic operations. Our goal is to isolate ( x ) to find its value, but before solving, we must simplify the expression by expanding and combining like terms.", "## Step 1: Combine Like Terms", "Look at the terms containing ( x ): ( 20x ) and ( -35x ). Combine these first:\n[\n20x - 35x = -15x\n]", "Now rewrite the equation with simplified variable terms:\n[\n-15x + 5250 = 4000\n]", "This step simplifies the equation and makes solving for ( x ) more straightforward.", "## Step 2: Isolate the Variable Term", "Now, subtract 5250 from both sides of the equation to move the constant to the right:\n[\n-15x = 4000 - 5250\n]", "Calculate the right side:\n[\n-15x = -1250\n]", "This step eliminates the constant, bringing us closer to solving for ( x ).", "## Step 3: Solve for ( x )", "Divide both sides by ( -15 ):\n[\nx = \frac{-1250}{-15} = \frac{1250}{15}\n]", "Simplify the fraction:\n[\nx = \frac{250}{3} \quad \ ext{or approximately} \quad x \approx 83.33\n]", "## Conclusion", "The solution to the equation ( 20x + 5250 - 35x = 4000 ) is:\n[\nx = \frac{250}{3}\n]", "Understanding how to expand, combine like terms, isolate variables, and perform arithmetic with negative numbers makes solving such equations more intuitive. Mastering these steps not only helps with algebra but also builds a strong base for higher-level mathematics.", "If you’re regularly solving equations like this, practice expansion, simplification, and careful calculation to keep your math skills sharp and confident."]