Solving equations

Solving equations

By Elliot Rogahn

So, What is an Equation?

​A equation si a mathematical statement that shows that two puantities are equal.

​ Example: 6 + 3 = 9​

In Algebra we usually see that one of the terms is unknown and a variable (letter) is used in it's place.

Example: x + 3 = 9​

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Addition Equations

Solve for x in the equation: x + 3 = 7

• We want to get x by itself, so we

want to remove the 3.

​

​

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x + 4 =7

​y + 5 = 12

Addition Equations

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Multiple Choice

Solve for x:

x + 2 = 9

• 7

• 5

• 9

• 11

Multiple Choice

Solve for x:

x + 4 = 4

• 0

• 8

• 2

• 4

Subtraction Equations

x - 4 = 7

• We want to remove the minus 4

• The opposite of minus 4 is plus 4

so I want to add ____ to BOTH

sides of the equation​

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​x -1 = 7

y - 3 = 5

Subtraction Equations

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Multiple Choice

Sovle for x:

x - 4 = 9

• 9

• 13

• 5

• 12

Multiple Choice

Solve for x:

x - 7 = 1

• 7

• 1

• 8

• -6

Multiplication Equations

These equations contain a coefficient. A coefficient is a number that is multiplied by the variable.

​

Therefore, we must remove the coefficient. Take a look at this equation: 3x = 9. Since there is no mathematical symbol between the 3 and the x we know that means multiplication. So, what number times 3 will give us an answer of 9? __ * 3 = 9​

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​3x = 18

What is the opposite of multiplication?

Multiplication Equations

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​-2y = 18

Multiplication Equations

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2x = 12

Multiple Choice

Solve for x:

4x = 16

• 4

• 12

• 20

• 3

Multiple Choice

Sovle for x:

5x = 40

• 8

• 10

• 45

• 35

Solving Two-Step Equations

Now that we know the rules for solving one-step equations, solving two-step equations will be easy!

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Each equation is going to be solved in two separate steps.

​2x + 3 = 43

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To get the x on the left by itself, we need to remove the 3 and the 2​

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2x + 3 = 43

We want to remove the 3 first.

Step 1:​

​

Step 2:​

Original Problem

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​3x +2 = 35

-5x - 4 = 46

Solving Two-Step Equations

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Multiple Choice

Solve for x

9x + 1 = 10

• 1

• 10

• 12

• 11

Multiple Choice

Solve for x:

6x - 5 = 7

• 2

• 3

• 6

• 12