Final answer:
The first step to solve the equation 4x + 3(x+2) = 5(2x-3) is to distribute the 3 and 5 to the terms inside the parentheses. Then, combine like terms and isolate the variable x to find the solution. In this case, x = 7.
Step-by-step explanation:
The reasonable first step to solve the equation 4x + 3(x+2) = 5(2x-3) is to distribute the 3 to (x+2) and distribute the 5 to (2x-3). This step is called the distributive property, which states that when we multiply a number outside parentheses by the sum inside the parentheses, we need to multiply the number with each term inside the parentheses. After distributing the numbers, the equation becomes 4x + 3x + 6 = 10x - 15.
Now, combine like terms on both sides of the equation. Add up the x terms and the constant terms separately. The equation becomes 7x + 6 = 10x - 15.
Move all the x terms to one side of the equation and the constant terms to the other side. Subtracting 7x from both sides, the equation becomes 6 = 3x - 15.
Continue solving the equation by isolating the variable x. In this case, add 15 to both sides of the equation. The equation becomes 6 + 15 = 3x, which simplifies to 21 = 3x.
Finally, divide both sides of the equation by 3 to solve for x. The equation becomes x = 7.
Learn more about One-Step Equations