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correctly select the order of the steps to solve this equation

-3/5(15x - 30) = 198

3 answers

To solve the equation \(-\frac{3}{5}(15x - 30) = 198\), follow these steps in the correct order:

  1. Eliminate the fraction: Multiply both sides by \(-\frac{5}{3}\) to get rid of the fraction and the negative sign.

    \[ (15x - 30) = 198 \times -\frac{5}{3} \]

  2. Simplify the right side: Calculate \(198 \times -\frac{5}{3}\).

  3. Distribute: Expand the left side if necessary, or you can directly solve for \(x\).

  4. Combine like terms: If the equation has like terms, combine them.

  5. Isolate \(x\): Solve for \(x\) by adding or subtracting terms as needed and dividing by the coefficient of \(x\).

  6. Check your solution: Substitute the value found for \(x\) back into the original equation to verify if both sides are equal.

By following these ordered steps, you should be able to find the value of \(x\) correctly.

so what is the answer

Let's go through the calculations step-by-step to solve the equation \(-\frac{3}{5}(15x - 30) = 198\).

Step 1: Eliminate the fraction

Multiply both sides of the equation by \(-\frac{5}{3}\) to eliminate the fraction:

\[ -\frac{5}{3} \cdot -\frac{3}{5}(15x - 30) = -\frac{5}{3} \cdot 198 \]

This simplifies to:

\[ 15x - 30 = -\frac{5 \cdot 198}{3} \]

Step 2: Calculate the right side

Now, compute \(-\frac{5 \cdot 198}{3}\):

\[ -198 \cdot \frac{5}{3} = -\frac{990}{3} = -330 \]

So we have:

\[ 15x - 30 = -330 \]

Step 3: Add 30 to both sides

Next, add 30 to both sides to isolate the term with \(x\):

\[ 15x = -330 + 30 \]

\[ 15x = -300 \]

Step 4: Divide by 15

Now, divide both sides by 15 to solve for \(x\):

\[ x = \frac{-300}{15} \]

\[ x = -20 \]

Final Answer

So the solution to the equation \(-\frac{3}{5}(15x - 30) = 198\) is:

\[ \boxed{-20} \]

Verification

To verify, substitute \(x = -20\) back into the original equation:

Original equation:

\[ -\frac{3}{5}(15(-20) - 30) = 198 \]

Calculating:

\[ -\frac{3}{5}(-300 - 30) = -\frac{3}{5}(-330) = \frac{3 \cdot 330}{5} = \frac{990}{5} = 198 \]

Since both sides are equal, our solution is confirmed. \(x = -20\) is the correct answer.