Solving Equations and Inequalities with One Variable

Equations Inequalities with One

Variable

​Objective

• To solve and Equation with only one variable.

• To solve an Inequality with only one variable.

Understanding the Equations

​A linear equation can be explained written in the form of AX + B = C or AX = B, where A, B, C are the constant terms and A= 0

​Example #1: 3x - 8 = 5x - 20

​-5x

​-5x

-​2x - 8 = -20

​+8

​+8

​-2x

​-2x

​-2x

​-2x

​x = 6

​The solution to the equation is 6.

​*Subtraction Property (Subtract 5x from both sides of the equation.)

​*Addition Property (Add 8 to both sides of the equation.)

​*Division Property (Divide both sides of the equation by -2.)

​Example #2: -7x - 9 = 2x +3

+9

​+9

-​7x = 2x +12

​-2x

​-2x

-9x = 12

​*Addition Property (Add 9 to both sides of the equation.)

​*Subtraction Property (Subtract -2x from both sides of the equation.)

​*Division Property (Divide 12 by -9.)

​x = 12

​-9

​x = -1

​1

​3

​*Simplify

Multiple Choice

Bellringer:

8 + x = -8

• x = -22

• x = 14

• x = -16

• x = -12

Multiple Choice

Solve the following Equation.

8x - 12 = 6x

• x = 9

• x = 6

• x = -4

• x = -1

Multiple Choice

Solve the following Equation.

3(x+2) = 18

• x = 6

• x = 3

• x = 4

• x = 0

Solving Inequalities Using One Variable

​Example #1: x + 4 ≥ 9

​*Subtraction Property(Subtract 4 from both sides of the inequality.

​*Simplify

​-4

​-4

​x ≥ 5

x

​*Multiplication Property(Multiply 5 by both sides of the inequality.

​̅

​5

​> 4

​Example #2:

​*5

*5

​x > 5 * 4

*Simplify

x > 20

Multiple Choice

Solve the following Inequality.

3x + 4 > 10

• x ≤ 3

• x > 2

• x > -5

• x > -6

Multiple Choice

Solve the following Inequality.

5x - 3 > -18

• x > 22

• x > -3

• x > 5

• x > 2

Multiple Choice

Exit Ticket:

-3 (-2x-2) > 21 + 3x

• x ≤ 5

• x > -3

• x < 3

• x > 5