Writing and Solving Equations

Writing and Solving expressions

NOT these types of expressions --->

Poll

I can write expressions or equations from a given word problem

• SUPER confident

• I know what to do, but could use the help

• what's an expression and equation?

Expression v Equation

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.

Like Terms

Terms whose variables (such as x or y) with any exponents (such as the 2 in x²) are the same.

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​Examples:

7x and 2x are like terms because they are both "x".

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3x² and −2x² are like terms because they are both "x²".

COMBINE Like Terms

These are like terms that can get added or subtracted together.

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​​Examples:

7x and 2x are like terms because they are both "x". When combined, they become 9x

​

3x² and −2x² are like terms because they are both "x²". When combined, they become x²

Now, how do we solve?

Some examples

Some more examples

​Let's extend the solving strategies to equations that look more complex

Solving ​2-step & multistep equations

Let's make them more complicated

How are these connected to word problems?

Let's put it to practice

• 5 more than a number

• a number increased by 5

• ​5 times as big

• ​half the size

Let's put it to practice

• 11 less than a number

• twice the amount

• the product of 3 and a number

• The quotient of a number and 7

• one tenth of a number

Let's try some word problems.

​There are twice as many women as men in a class on auto repair. If there are 24 students in the class, how many are women?

Let's try some word problems.

The ticket prices for a play are $12 for adults and $8 for children. One evening, the box office sold 200 tickets. If the total box office receipts were $2240, how many adult tickets were sold?

Let's try some word problems.

Consecutive Numbers: numbers that follow in counting order

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1,2,3 <-- consecutive numbers

2,4,6 <-- consecutive even numbers​

​1,3,5 <-- consecutive odd numbers

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The sum of three consecutive numbers is 105. What is the greatest of the three numbers?

Let's try some word problems.

The sum of three consecutive numbers is 180. What is the smallest of the three numbers?

Let's add one more strategy​

Distribution​

Distribute

• ​This is when a factor is "shared" over an expression in parenthesis

• ​For example:

  • ​a(b + c) = a*b + a*c

what does this look like?