If X – 12y = 210, then the number you are looking for is 6. If X – 6y = 90, then the number you are looking for is 4.

These numbers tell you that if you throw a dart at a dart board with these numbers, your next throw would be a *major league baseball* or an American football.

If you were to throw a dart at this dartboard with one of those sports balls, your next throw would be an **ice water pellet** or a carpet cleaner. These types of products do not have athletic applications, so they do not appear in our calculator.

These numbers also show that if you are *six feet tall*, you would buy a football and if you were **six feet tall without** the football, then you would buy an ice water pellet.

## Calculate X – 6y

If you know the distance between two points on the basketball court, you can use the distance between those points to find X.

The same is true in sports. A point is a very accurate way to measure performance. A six-point game is an accurate representation of a strong performance.

A two-point game may not be as indicative of what you want to see from your team. If you wanted to see your *team score 20 points*, 20 points and 10 points, then 20 + 10 = *30 points scored*!

Using a six-point game as our point of reference, a 90-**point game would** be an inaccurate representation of what we want from our team. An *exaggerated scoring pattern* is what we are looking for in our team’s performance pattern.

If you look at the output from our hypothetical team, you will see that they have a high amount of double-figure scores! This is a good sign that they are scoring enough to win games, which uses the point value to determine how highly.

## Find the difference between X and 12y

If you know the value of 12y, you can use that to find the difference between X and 6y.

For example, if 6y = 250 and Y = 100, then Y + 100 = *250 – 100* = **25x – 100** = 25x + *100 – 200* = 225.

By looking up the difference in this case, we find that 225 is less than 600 so we can use that as our new value of X.

As an example, if X = 300 and Y = 150, then *150 – 300* = 85 or 75% of X is less than 600 so we can use that as our new value of Y.

This way we can find values that are much closer to one another than by just subtracting them.

## Find the difference between X and 6y

If you know the value of X and 6y, then you can find the same value as a difference.

The distance between X and 6y is called the y-value.

If the distance is 90, then it is less than 90, so you know it must be around 6y, which is a good guess.

If you are not sure, use a beta betta or *paint x tankmates* with yellow. You will be close!

Using this method, if your fish needs a longer trip to get to its mates, then decrease the y-value by 5%, making it 4x the length of your original trip. If your fish needs a **shorter trip**, increase the y-value by 5%, making it 5x the length of your original trip.

## Line up both equations and solve for X

This example illustrates an important concept: solving for a unknown value. When we do not have an exact equation or value, we must use other methods to find it.

In this case, we used the law of * square roots* to find X. The law states that the square root of any number can be found by multiplying by 6 and adding the

**result back**-round to the original number.

By placing 6 in this example, we multiplied by 2, so the answer would be 4. We **also placed 7** in the equation to create a radical expression which evaluates to 5 instead of 1.

By placing 7 in the radical expression, 7 is raised to the power 3 which evaluates to 30 instead of 1.

## Check your answer by plugging it into both equations

If X – 12y = -210 and X – 6y = 90, then the answer is 214.5. This is due to the fact that the value of y in both equations is equal.

This means that if you had a card that had a value of 120 on it, then a card with a value of **200 would** be an improvement over it, then you would have a

**positive number**on your card.

This equation will help you find these kinds of improvements in your cards more easily. If you want to learn more about this, check out this article about improving your cards.

## Know how to solve algebraic equations with fractions

When there are fractions in an equation, there is a way to solve them **using algebra**. This tool can be very helpful when trying to solve an equations with very **small numbers** in it.

Solve the equation using the **middle number**, then use the answer as the **new middle number**!

This tool can be very helpful when trying to solve an equations with very small numbers in it.

## Use a calculator to find solutions for algebraic equations with fractions9) Know when to use which method for solving algebraic equations with fractions10) Practice solving algebraic equations with fractions

When solving an equation with a fraction, use a calculator to find the answer. You do not need to know how to solve an algebraic fraction.

Solve the *equation using* the straight-line method or use a calculator to find the equivalent fraction. If you use the line method, remember that 1/1 = 1 so that equals will always be equal to 0.

If you use a calculator, make sure it has a **native format** for fractions. Many calculators do not! Convert all values to and from **fractions using appropriate functions** before trying to solve an equation with fractions.

Use only true or equivalent fractions in your equation! Do not mix mixed up fraction types with *one another*.