Question

solve the equation \\(\frac{x}{3} + 6 = 15\\) for \\(x\\). show your work by filling in the boxes below with the appropriate equations and actions (in words) to describe what you did in that step of the process of solving the equation. - drag the initial equation to column 1, row 1 of the grid: \\(\frac{x}{3} + 6 = 15\\). - note: the
esulting equation after action\ for row 1 will be used again as the \starting equation on this step\ for row 2. \\(\boldsymbol{\downarrow}\\) | | starting equation on this step | action (in words) | resulting equation after action | | --- | --- | --- | --- | | step 1 | | | | | step 2 | | | | \\(\boldsymbol{\downarrow}\\) equations \\(\boldsymbol{\downarrow}\\) - \\(x = -1\\) - \\(x = 3\\) - \\(x = 7\\) - \\(x = 27\\) - \\(x = 39\\) - \\(x = 63\\) - \\(\frac{x}{3} = 9\\) - \\(\frac{x}{3} = 21\\) - \\(x + 6 = 5\\) - \\(x + 6 = 45\\) - \\(\frac{x}{3} + 6 = 15\\) \\(\boldsymbol{\downarrow}\\) action (in words) \\(\boldsymbol{\downarrow}\\) - add 6 to both sides of the equation. - subtract 6 from both sides of the equation. - divide both sides of the equation by 3. - multiply both sides of the equation by 3.

Explanation:

Step 1:

Starting Equation: $\frac{x}{3} + 6 = 15$
Action: Subtract 6 from both sides of the equation.
To solve for $x$, we first isolate the term with $x$. Subtracting 6 from both sides eliminates the constant term on the left.
Calculation: $\frac{x}{3} + 6 - 6 = 15 - 6$
Resulting Equation: $\frac{x}{3} = 9$

Step 2:

Starting Equation: $\frac{x}{3} = 9$
Action: Multiply both sides of the equation by 3.
To solve for $x$, we multiply both sides by 3 to cancel the denominator.
Calculation: $\frac{x}{3} \times 3 = 9 \times 3$
Resulting Equation: $x = 27$

Answer:

Step	Starting Equation on This Step	Action (in Words)	Resulting Equation After Action
2	$\boldsymbol{\frac{x}{3} = 9}$	Multiply both sides of the equation by 3.	$\boldsymbol{x = 27}$