Solving Equations by Using Models

Senin, 13 Maret 2023

Many real-world situations can be approached by developing a model, writing an equation, and solving it. You can use algebra tiles to solve equations. The green tile represents the variable, x.

 

Example

 

1.     Use algebra tiles to solve each equation.

x + (–2) = –7

 

Alternative Solutions :

 

Step 1     Model x + (–2) = –7 by placing 1 green tile and

2       red square tiles on one side of the mat to

represent x + (–2). Place 7 red square tiles on the

          other side to represent –7.

 

Step 2     To get the green tile by itself, remove 2 red

square tiles from each side.

 

Step 3    The green tile on the left side of the mat is matched

with 5 red square tiles.

         Therefore, x = –5.

 

2.     x – 3 = 5

 

Alternative Solutions :

 

Step 1     Write the equation in the form x + (–3) = 5. Place

green tile and 3 red square tiles on one side of the mat

to represent x + (–3). Place 5 yellow square tiles on the

other side of the mat to represent +5.

 

Step 2    To get the green tile by itself, you need to remove 3

           red square tiles from each side. Since there are no

           red square tiles on the right side of the mat, you

           will need to add 3 yellow square tiles to each side to

           make 3 zero pairs on the left side of the mat.

Step 3   Remove the zero pairs.

 

Step 4   The green tile is matched with 8 yellow square tiles.

Therefore, x = 8.

 

In Examples 1 and 2, you solved each equation for the variable by isolating the variable on one side of the equation.

 

Example

Zoology Link

 

3.   The largest bear is the Alaskan brown bear. When fully grown, it has a height of 9 feet. The smallest bear is the sun bear. The Alaskan brown bear is 6 feet longer than the sun bear. Find the length of the sun bear.

 

Alternative Solutions :

 

Explore             You know that the Alaskan brown bear is 6 feet

longer than the sun bear. You need to find the length

of the sun bear.

 

Plan                  Let x represent the length of the sun bear. Translate the

problem into an equation using the variable x.

Model the equation and then solve.

 

Solve              

                        

 

To solve for x, subtract 6 from each side.

 

 

The solution is 3. So, the length of the sun bear is 3 feet.

 

Examine      Check the solution.

The length of the Alaskan brown bear is equal to the length

of the sun bear plus 6 feet. The length of the sun bear is 3 feet,

and 3 feet plus 6 feet is 9 feet.

The answer is correct.

 

 

Sumber

Labels: Mathematician

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