Solving Equations with Variables on Both Sides (Day 2)

Solving Equations with Variables on Both Sides (Day 2)

Objective

Objective: Students will be able to identify solution types and solve equations with variable on both sides using properties of equality, combining like terms, and the distributive property.

Standards

Colorado 8th Grade Math Equations and Expressions Standards: 8.EE.C.7.a: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 8.EE.C.7.b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Solving Equations With Variables on Both Sides

• Write the Equation

• Use Inverse Operations to move the variable terms to one side of the equation

• Use Inverse Operations to move the constant terms to the other side of the equation

• Divide by the coefficient to isolate the variable

Multiple Choice

What is the first step to solve this equation:

11 - 3x = 44

• Add 3 to both sides

• Subtract 11 from both sides

• Add 11 to both sides

• Divide 3 on both sides.

Multiple Choice

What is the first step to solve this equation:

10 + 7x = 44 -2x

• Add 2x to both sides

• Subtract 2x from both sides

• Add 10 to both sides

• Divide 7 on both sides.

Multiple Choice

-5k + 10 = -2k - 14

• k = 8

• k = -8

• k = 2

• k = -2

Multiple Choice

Solve for f:
f - 4 = 6f + 26

• f = -5
• f = 5
• f = 6
• f = -6

Multiple Choice

Solve for x:
5x - 14 = 8x + 4

• x = 6
• x = -6
• x = -18/13
• x = 10/3

The Distributive Property

• Use the Distributive property to simplify one side of the equation first if needed.

• addition: $a\left(b+c\right)=ab+ac$ 

•  subtraction:  $a\left(b-c\right)=ab-ac$ 

Multiple Choice

Solve:
5y+34 = -2(-7y+1)

• y = -4
• y = 9
• y = 4
• y = 36/19

Solution Types

• One solution: variable = a number $\left(x=4\right)$   

• No solution: variables cancel and you have a number = a different number  $\left(4=7\right)$  

• Infinitely Many Solutions: variables cancel and you have a number = same number  $\left(4=4\right)$  

Multiple Choice

 $7x-3=7x+5$  

• No Solution

• Infinite Solutions

•  $x=2$  

•  $x=8$  

Multiple Choice

5x + 6 = 2 + 3x

• one solution x = -2

• no solutions

• infinite solutions

• one solution x = 2

Multiple Choice

 $6x+5=8+4x+2x$  

• No Solution

• Infinite Solutions

•  $x=3$  

•  $x=13$  

Multiple Choice

3x + 15 = 3(x + 5)

• No Solution
• x = 15
• Infinitely Many Solutions

Multiple Choice

6x - 8x + 5 = -2(x + 2) + 7

• One solution

• No solution

• Infinitely Many