High School

Select the correct answer.

Create and solve a linear equation that represents the model, where circles and a square are shown evenly balanced on a balance beam.

A. [tex]x + 7 = 12 ; x = 5[/tex]
B. [tex]x = 5 + 7 ; x = 12[/tex]
C. [tex]x + 7 = 5 ; x = -2[/tex]
D. [tex]x + 5 = 7 ; x = 2[/tex]

Answer :

We start by representing the balance with the equation

[tex]$$x + 7 = 12.$$[/tex]

This equation models the scenario: one side has a weight of [tex]$x$[/tex] (for example, representing circles) plus an additional weight of 7 (for example, representing a square), and the other side has a total weight of 12.

Step 1. Isolate the variable

Subtract 7 from both sides to solve for [tex]$x$[/tex]:

[tex]$$
x + 7 - 7 = 12 - 7.
$$[/tex]

Step 2. Simplify the equation

Simplifying gives:

[tex]$$
x = 5.
$$[/tex]

Since [tex]$x = 5$[/tex] satisfies the equation, the correct linear model is

[tex]$$x + 7 = 12 \quad \text{with} \quad x = 5.$$[/tex]

Thus, the correct answer is:

[tex]$$\boxed{x+7=12 ;\quad x=5.}$$[/tex]

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