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correctly select the order of the steps to solve this equation

1/3 (6x-9)=-33

3 answers

To solve the equation \( \frac{1}{3}(6x - 9) = -33 \), follow these steps in order:

  1. Multiply both sides by 3 to eliminate the fraction: \[ 6x - 9 = -99 \]

  2. Add 9 to both sides to isolate the term with \( x \): \[ 6x = -90 \]

  3. Divide both sides by 6 to solve for \( x \): \[ x = -15 \]

So the correct order of steps to solve the equation is:

  1. Multiply both sides by 3.
  2. Add 9 to both sides.
  3. Divide both sides by 6.
do it again but with these answers
a. add 9 to both sides of the equation
b. add 1/3 to both sides of the equation
c. divide by 6 on both sides of the equation
d. subtract 1/3 from both sides of the equation
e. divide by 1/3 from both sides of the equation
f. multiply by 1/3 on both sides of the equation
g. subtract 6 from both sides of the equation
h. subtract 9 from both sides of the equation
i. multiply by 6 on both sides of the equation

To solve the equation \( \frac{1}{3}(6x - 9) = -33 \) using the provided options, the correct order of steps is as follows:

  1. Multiply by 3 on both sides of the equation to eliminate the fraction (equivalent to multiplying by the reciprocal of \( \frac{1}{3} \)):

    • This is not listed explicitly; however, if we were to mimic this, we could think of multiplying both sides by 3 to lead to the next step.

  2. Subtract 9 from both sides of the equation (Option h):
    From \( 6x - 9 = -99 \): \[ 6x = -90 \]

  3. Divide by 6 on both sides of the equation (Option c): \[ x = -15 \]

The sequence of applicable answers is:

  1. Start with Step f (though it isn't directly listed, it's the action equivalent to multiplying both sides by 3).
  2. Step h: Subtract 9 from both sides.
  3. Step c: Divide by 6 on both sides.

Since f may not appear explicitly in the choices, the closest path to solving the equation with the provided options would be:

  • Use Step h: Subtract 9.
  • Use Step c: Divide by 6.

Note that the multiplication step to eliminate the fraction must occur but is not represented clearly in the answer choices you provided.