Question

solve the equation \\(\frac{1}{2}x + 7 = 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{1}{2}x + 7 = 15\\). - note: the
esulting equation after action\ for row 1 will be used again as the \starting equation on this step\ for row 2. step 1 starting equation on this step action (in words) resulting equation after action step 2 starting equation on this step action (in words) resulting equation after action equations: \\(x = 44\\), \\(x = 4\\), \\(x = 11\\), \\(x = 16\\), \\(\frac{1}{2}x = 8\\), \\(\frac{1}{2}x = 22\\), \\(\frac{1}{2}x + 7 = 15\\) action (in words): add 7 to both sides of the equation, divide both sides of the equation by 2, multiply both sides of the equation by 2, subtract 7 from both sides of the equation.

Explanation:

Step 1:

Starting Equation: $\frac{1}{2}x + 7 = 15$

Action: Subtract 7 from both sides of the equation.

Resulting Equation: $\frac{1}{2}x = 8$ (because $15 - 7 = 8$)

Step 2:

Starting Equation: $\frac{1}{2}x = 8$

Action: Multiply both sides of the equation by 2.

Resulting Equation: $x = 16$ (because $\frac{1}{2}x\times2 = x$ and $8\times2 = 16$)

So filling the table:

• Step 1:
• Starting Equation on This Step: $\frac{1}{2}x + 7 = 15$
• Action (in Words): Subtract 7 from both sides of the equation.
• Resulting Equation After Action: $\frac{1}{2}x = 8$

• Step 2:
• Starting Equation on This Step: $\frac{1}{2}x = 8$
• Action (in Words): Multiply both sides of the equation by 2.
• Resulting Equation After Action: $x = 16$

Answer:

The solution to the equation $\frac{1}{2}x + 7 = 15$ is $x = 16$.