PreAlgebra Q3W6: Review: Solving linear equations with one variable.

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Presentation transcript:

PreAlgebra Q3W6: Review: Solving linear equations with one variable

Objective I can solve linear equations with rational number coefficients by combining like terms. I can give examples of linear equations with one solution, no solution, and infinitively many solutions.

Vocabulary Constant A number with nothing else attached to it. Examples: 1, 2, 47, 925 Variable A letter that represents an unknown number. Examples: a, b, x, y Coefficient The number in front of the variable. Examples: 3x 3 is the coefficient 2x 2 is the coefficient 2x 2 is the coefficient

Like Terms: Terms that have the same variables, raised to the same powers (same exponents).

These are “unlike terms” 17x, 17z 15y, 19y², 31y 5 Like terms must have the SAME variable raised to the SAME power.

Like Terms, or Not? 2x and 3y 4x and 4x 2 6x and 7x 8 and 5y Yes/no

Like Terms are Important Because we can combine like terms. We cannot combine unlike terms!

5 cats + 3 cats 5a + 3a = 8 cats

5 apples + 3 oranges

Combining Like Terms 6x + 2x = When combining like terms, add (or subtract) the coefficients. 6x + 2x =8x Simplify: Key Skills

Practice Combining Like Terms x + x 2x + 3x 6y + 7y 5x - x + 7y

Practice Combining Like Terms 6x + 4x x + x + 1 5x – 2x + 4x x - 1

Solving Linear Equations Warm up: Solve for X: 1.6x = X = x + 5 = 23

Linear Equations: How Many Solutions? Usually, an equation will have just ONE SOLUTION. There are 2 exceptions: 1)No Solutions 2)Infinite Solutions

Infinite Solutions When one side of an equation is identical to the other side, then there are infinite solutions. Example: 3x = 3x Whatever you plug in for “x” will work.

Examples with Infinite Solutions 2x = 2x 3x = 2x + x 4x + 1 = 4x + 1

No Solutions If you have an equation and you end up with unequal values on each side of the equation, there are no solutions. (This is true when x does NOT = 0) Example: 4x = 6x There is no value for “x” that will make this true.

Examples with No Solutions (when x does NOT = 0) 8x = 3x x + 4 = x = 2 + x

Infinite Solutions, or No Solutions? 4x = 4x 5x + 1 = 5x + 1 6x = 4x 2x = x Infinite/None

In Class Practice Problems 1)4x + 3 = 23 2) 8x + 2 = 34

In Class Practice Problems 3) 3x + 4 = 3x + 5 4) 2x + 1 = 2x + 1

In Class Practice Problems 5) 3x + 4 = 2x + 7 6) 5x + 3x + 2x + 8 = 18x