Why Is It Important To Know How To Compare The Values Algebraically? Cite Some Practical Application

Why is it important to know how to compare the values algebraically? Cite some practical applications.

 

Answer:

Comparison Method for Math Problems

Compare a comic book to the film about the same superhero. How are they the same and how are they different? Its fun doing these types of comparisons.

In math, we can also do comparisons. We can use the comparison method, a procedure to solve for the unknowns in a set of independent equations:

Lets take the equations 2x + 3y = 13 and 7x - 4y = 2. How do we solve for x and y?

We set up the equations so the left-hand sides have the same unknown variable. Thus, the left-hand sides are the same. Then we equate the right-hand sides and solve. In this lesson, we will clearly show the steps. Then we can get back to the adventures of our favorite superhero.

The First Equation

We want to solve for x and y given the two equations 2x + 3y = 13 and 7x - 4y = 2.

Step 1: write each equation with x as the subject. We will call this the isolated-subject equation, an equation where one variable is isolated. From 2x + 3y = 13, we subtract 3y from both sides:

2x + 3y - 3y = 13 - 3y

Then simplify:

2x = 13 - 3y

Divide both sides by 2:

2x/2 = (13 - 3y) / 2

Then simplify:

x = (13 - 3y) / 2

We have isolated the x in the first equation.

The Second Equation

Now for the second equation. From 7x - 4y = 2, we add 4y to both sides:

7x - 4y + 4y = 2 + 4y

Then simplify:

7x = 2 + 4y

Divide both sides by 7:

7x / 7 = (2 + 4y) / 7

Simplify and we have:

x = (2 + 4y) / 7

We have isolated the x in the second equation.

Compare

Step 2: Now we can compare the left-hand sides of both isolated-subject equations. They are the same: both equal x. Since x = (2 + 4y) / 7 and x also = (13 -3y) / 2 we can equate the right-hand side of the first isolated-subject equation to the second. So now we know that:

(13 - 3y) / 2 = (2 + 4y) / 7

Step 3: we solve for the remaining variable, y. First, we multiply both sides by 2:

2(13 - 3y)/2 = 2(2 + 4y) / 7

When we simplify, we have:

13 - 3y = (4 + 8y) / 7

Multiply both sides by 7:

7(13 - 3y) = 7(4 + 8y) / 7

When we simplify, we have:

91 - 21y = 4 + 8y

Subtract 8y from both sides:

91 - 21y - 8y = 4 + 8y - 8y

Simplify, and we have:

91 - 29y = 4

Subtract 91 from both sides:

91 - 29y - 91 = 4 - 91

When we simplify, we have:

-29y = - 87

Divide both sides by -29:

-29y / (-29) = -87 / (-29)

And when we simplify we are left with:

y = 3

Now that we have a value for y, we can find the value of x.

Step 4: substitute our value for y into either of the isolated-subject equations. Lets substitute y = 3 into x = (13 - 3y) / 2. So:

x = (13 - 3(3)) / 2

Simplify this equation:

x = (13 - 9) / 2

x = 4 / 2

x = 2

Now we have a result:

x = 2 and y = 3

Step-by-step explanation:

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