Simplifying and Solving Equations Steps for Combining Like

Simplifying and Solving Equations

Steps for Combining Like Terms • Identify the items which are “Like Terms. ” • Rewrite the expression so that the like terms are all next to each other. • Combine the groups of like terms together to make a simplified shorter final answer. This last step involves adding or subtracting the like terms.

Combining Like Terms • People who are twins are a “like pair” because they have the exact same features.

Definition of Like Terms • Like Terms are terms that contain the same letter variables which are raised to the exact same powers.

Like Terms or Not Decide if the terms in each pair are “Like Terms. ” • •

Why We Combine Like Terms • When we combine like terms, we keep the items together to make a simplified list. § It’s just like a family ordering a meal. It is easier to place a combined order rather than individual orders.

Algebraic Take Out Consider the following order: • 2 Spicy Avocado Vegie Burgers • 1 Sweet Potato Fry • 1 Drink • 3 Spicy Avocado Vegie Burgers • 2 Sweet Potato Fries • 2 Drinks

Multi-Step Equations • You can solve equations that require more than two steps. They are called multi-step equations. If there are like terms on one side of an equation, first use the Distributive Property to combine them. Then use the properties of equality to solve the equation.

Simplifying and Solving Equations • An equation may have like terms on one or both sides of the equal sign. To solve the equation, you want to isolate the variable. • The first step is to combine like terms. •

Fund Raising • The 24 students in your class have pledged to collect 1, 200 returnable bottles to raise money for the vertical garden. During the first week, each student collected 34 bottles. How many more bottles must each student collect?

Fund Raising Cont’d •

Variables on Both Sides – Word Problems § An electrician charges $250 base plus $16 per hour. Another electrician charges $210 base plus $18 per hour. How long is a job for which the two companies costs are the same?

Variables on Both Sides – Word Problems How to set up the equation • How to solve •

UPS charges $7 for the first pound, and $0. 20 for each additional pound. Fed. Ex charges $5 for the first pound and $0. 30 for each additional pound. How many pounds, p, will it take for UPS and Fed. Ex to cost the same?

How to Setup the Equation

The Solution •

A twelve inch candle and an 18 inch candle are lit at 6 pm. The 12 -in. candle burns 0. 5 inches every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the same height? Let h represent the number of hours.

The Setup and Solution • •

Geometric Algebra

Extra Practice •

Extra Practice Continued •

A Container Conundrum • Container A has 200 L of water, and is being filled at a rate of 6 liters per minute. Container B has 500 L of water, and is being drained at 6 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water?

An 500 liter intermediate bulk container (IBC), or pallet tank, is a reusable industrial container designed for the transport and storage of bulk liquid and granulated substances, such as chemicals, food ingredients, solvents, pharmaceuticals, etc. Here it is being used as a home rain barrel.

The Container Solution • It will take 50 minutes for the containers to have equal amounts of water.

The Final Four • Answers are on the next slide for you to check your work. However, be sure to show your work for credit on the notebook check.

The Results •

Any Questions…