Questions: Solve: 0.24(100 x+5)=0.4(30 x+15). x=

Solution Steps

To solve the equation \(0.24(100x + 5) = 0.4(30x + 15)\), we need to follow these steps:

1. Distribute the constants inside the parentheses.
2. Simplify both sides of the equation.
3. Isolate the variable \(x\) by moving all terms involving \(x\) to one side and constant terms to the other side.
4. Solve for \(x\).

We start with the equation: \[ 0.24(100x + 5) = 0.4(30x + 15) \] Distributing the constants gives: \[ 24.0x + 1.2 = 12.0x + 6.0 \]

Next, we move all terms involving \(x\) to one side and constant terms to the other side: \[ 24.0x - 12.0x = 6.0 - 1.2 \] This simplifies to: \[ 12.0x = 4.8 \]

Now, we divide both sides by \(12.0\): \[ x = \frac{4.8}{12.0} = 0.4 \]

Final Answer