Work Step by Step
The equation is true because the expression on the right side of the equal sign is equivalent to the expression on the left side of the equal sign. We can show this by simplifying the left side of the equation. Once simplified, the left side will match the right side if they are equal. x - 0.02(x + 200) = 0.98x - 4 Step 1: distribute the 0.02 across the expression in parenthesis. x - 0.02x - 4 = 0.98x - 4 Note: The minus sign to the left of 0.02 in the original writing of the problem is used in the multiplication of the distributive property. -0.02 times x gives us the -0.02x. The -0.02 times 200 gives us the -4. Step 2: Write x as 1.00x. The x leading off on the left side of the equation is considered to be “one x” or 1x. If the coefficient of a variable is exactly 1, we typically don’t write it. Writing it here allows us to see it and it helps to prevent errors in our addition/subtraction. 1.00x - 0.02x - 4 = 0.98x - 4 Step 3: Combine like terms on the left side of the equation. 1.00x - 0.02x gives us 0.98x 0.98x - 4 = 0.98x - 4 The left side matches the right side, so the original equation showed us a true statement/equation.