To solve the equation \( 24(34+x) = 1,200 \) and explain each step, let's break down what happens at each point:
Step 1: \( 24(34+x) = 1,200 \) is expanded to \( 816 + 24x = 1,200 \).
- Reason: The left side of the equation \( 24(34 + x) \) is simplified by using the distributive property, which states that \( a(b + c) = ab + ac \). Here, \( 24 \cdot 34 = 816 \) and \( 24 \cdot x = 24x \), leading to \( 816 + 24x = 1,200 \).
Step 2: \( 816 - 816 + 24x = 1,200 - 816 \).
- Reason: Subtraction is used to isolate the term involving \( x \) on one side of the equation. By subtracting \( 816 \) from both sides, we maintain equality (as per the properties of equations: whatever you do to one side, you must do to the other). This simplifies to \( 24x = 1,200 - 816 \).
Step 3: Simplification yields \( 24x = 384 \).
- Reason: The right side of the equation \( 1,200 - 816 \) is calculated, giving \( 384 \). Thus, the equation simplifies to \( 24x = 384 \).
Step 4: \( x = 16 \).
- Reason: To solve for \( x \), divide both sides of the equation \( 24x = 384 \) by \( 24 \). This uses the principle of isolation of the variable by performing the same operation (division in this case) on both sides of the equation. The result is \( x = \frac{384}{24} \), which simplifies to \( x = 16 \).
Thus, the solution for the equation \( 24(34+x) = 1,200 \) is \( x = 16 \).