solve for x in the equation 102.5(x-11.92)=71.6. round 3 decimal places

Answer 1

To solve the equation \( 102.5(x - 11.92) = 71.6 \), follow these steps:

1. Distribute \( 102.5 \) on the left side of the equation:

\[ 102.5x - 102.5 \times 11.92 = 71.6 \]

Calculating \( 102.5 \times 11.92 \):

\[ 102.5 \times 11.92 \approx 1226.69 \]

Now, substituting that back into the equation:

\[ 102.5x - 1226.69 = 71.6 \]

2. Add \( 1226.69 \) to both sides:

\[ 102.5x = 71.6 + 1226.69 \]

Calculating the right side:

\[ 71.6 + 1226.69 \approx 1298.29 \]

So, we have:

\[ 102.5x = 1298.29 \]

3. Divide both sides by \( 102.5 \):

\[ x = \frac{1298.29}{102.5} \]

Calculating that division:

\[ x \approx 12.66 \]

Rounding \( x \) to three decimal places gives us:

\[ \boxed{12.661} \]

Answer 2

are u sure

Answer 3

Let's go through the calculations step-by-step again to ensure accuracy.

Given the equation:

\[ 102.5(x - 11.92) = 71.6 \]

1. Distribute \( 102.5 \) on the left side:

\[ 102.5x - 102.5 \cdot 11.92 = 71.6 \]

Calculating \( 102.5 \cdot 11.92 \):

\[ 102.5 \cdot 11.92 = 1226.69 \]

So now we update the equation:

\[ 102.5x - 1226.69 = 71.6 \]

2. Add \( 1226.69 \) to both sides:

\[ 102.5x = 71.6 + 1226.69 \]

Calculating the right side:

\[ 71.6 + 1226.69 = 1298.29 \]

So we have:

\[ 102.5x = 1298.29 \]

3. Now, divide both sides by \( 102.5 \):

\[ x = \frac{1298.29}{102.5} \]

Calculating the division:

\[ x \approx 12.66 \]

When performing the division:

\[ x \approx 12.661 \]

Thus, rounding \( x \) to three decimal places gives:

\[ \boxed{12.661} \]

I can confirm that the previous result is correct. If you have any further questions or need additional assistance, feel free to ask!