Question

What value in the replacement set is a solution to this equation? 3(n+7)=48 Replacement set: 8, 9, 10, Drag the solution into the box. Put responses in the correct input to answer the question. Select a response, navigate to the desired input, and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button, or touchpad. Responses can also be moved by dragging with a mouse.

Answer 1

The solution set is {9}.

Explanation:

The replacement set for an equation is the set of values that may be substituted for the variable.

Given equation:

`3(n+7)=48`

Given replacement set:

• {8, 9, 10}

The solution set is the set of all values that make the equation true.

To find the solution set from the replacement set, input each value from the replacement set and evaluate both sides of the equation. If the two sides are equal, the equation is true and the value is a solution.

`\begin{aligned}n=8 \implies 3(8+7)&=48\\3(15)&=48\\45&=48\\\end{aligned}`

As 45 ≠ 48, n=8 is not a solution.

`\begin{aligned}n=9 \implies 3(9+7)&=48\\3(16)&=48\\48&=48\\\end{aligned}`

As both sides are equal, the equation is true and n=9 is a solution.

`\begin{aligned}n=10 \implies 3(10+7)&=48\\ 3(17)&=48\\51&=48\\\end{aligned}`

As 51 ≠ 48, n=10 is not a solution.

Therefore, the solution set is {9}.

Answer 2

• n = 9

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Given

• Equation 3(n + 7) = 48

Solve it and compare the solution with replacement set

• 3(n + 7) = 48
• n + 7 = 48/3
• n + 7 = 16
• n = 16 - 7
• n = 9

The solution is one of the elements of the replacement set.