5.3: Solving Linear Equations Symbolically

I can solve a given linear equation symbolically.
I can verify by substitution whether a given rational number is a solution to a given linear equation.

Bell Ringer

What should you do next?

Complete the next step to solve this equation:

4x + 2 = 10

→ __________

Why do we do this?

What does this "undo" in the equation?

Complete the same process for each of these examples but try to solve for x.

5x - 3 = 12

x/4 + 6 = 10

Inverse Operation - An operation that undoes another

🟰Examples:

Isolate the Variable - To get the variable by itself on one side of the equation.

🟰 Example: 4x = 8 → divide both sides by 4 → x = 2

Solution - The value of the variable that makes the equation true.

🟰 Example: In x + 3 = 7, the solution is x = 4.

Substitution - Replacing the variable with a number to check if it makes the equation true.

🟰 Example: If x = 4, then check 4 + 3 = 7.

Simplify - To combine like terms or perform operations to make the equation easier to solve.

Satisfy an equation - to find a value for the variable that makes both sides of the equation equal.

Example: 3x - 1 = 9

Let x = 3

3(3) - 1 = 8

8 = 8 ✅ True

Therefore, x=3 satisfies the equation.

5.3 Lesson

Complete the following 2 questions on your handout and submit for assessment.

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