*Contributor: Stefani Allegretti. Lesson ID: 14180*

Finding the unknown in a multi-step equation with fractional coefficients is kind of like unlocking the key to a mathematical treasure! Get ready to find some hidden math treasures!

categories

subject

Math

learning style

Auditory, Visual

personality style

Otter, Golden Retriever

Grade Level

Intermediate (3-5)

Lesson Type

Quick Query

Treasure hunting is always fun.

Searching for hidden gems, treasure chests, and different artifacts of old is exciting and thrilling.

Just like finding a key that unlocks a hidden treasure, solving a multi-step equation with an unknown can also be super exciting!

The unknown in a mathematical equation is like a key that unlocks a math treasure!

Get ready to learn how to solve for an unknown in multi-step equations involving fractional coefficients!

Just like any treasure-hunting experience, there is a key that unlocks the treasure!

When solving for an unknown in multistep equations involving fractional coefficients, the key to unlocking the equation is finding the missing variable or unknown number, usually referred to as 'x.'

Take a look at the equation below.

1 | x | + | 3 | = | 12 |

6 |

- How can you find out what x equals?

Just like in a multi-step equation with an unknown, you first want to isolate the x.

- How do you do that?

First, simplify the equation by eliminating the +3.

You can eliminate the +3 by subtracting -3.

Remember to subtract 3 from both sides of the equal sign.

After you subtract 3 from the left side of the equation, you are left with 1/6x.

After you subtract 3 from the right side of the equation, you are left with 9.

So the simplified equation is:

1 | x | = | 9 |

6 |

- What should you do next?

Next, you must multiply by the inverse of ^{1}/_{6} on both sides of the equation.

1 | x | 6 |

6 | 1 |

So you are left with x = 9.

However, you still need to multiply ^{6}/_{1} by 9 on the right.

6 | x | 9 |

1 | 1 |

Since the denominators are both 1, multiply the numerators across.

6 x 9 = 54!

So your answer is 54!

After you solve for x, remember to verify your answer.

Simply plug your number back into the original equation to check it.

1 | x | 54 | + | 3 | = | 12 |

6 |

- Does it check out?

Yes, it does!

Check out this video to see a problem like this in action!

Nice work!

- What if you have to solve a multistep equation with a negative fraction?

- How does that work?

Watch the video below to find out!

Great work, math treasure hunter! You unlocked lots of math treasures.

Now, head to the *Got It? *section for more math treasure hunting!