Equations with Variables on Both Sides

Students will be able to:

• Solve linear equations that have variables on both sides.

• Identify special solutions of linear equations.

When solving equations with variables on both sides,

•  The goal is to get the variable on one side (isolate the variable) and the constants on the other sides.

• ** TIP * Always move the smallest coefficient first.

On your desk, solve the following question and I will be coming to check your work.

4x - 7 = -3x

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​Desktop Math

On our desk top, solve the following question:

​-3(w + 4) = 4w - 5

​-3(w + 4) = 4w - 5
-3w - 12 = 4w -5
+ 5 + 5
-3w - 7 = 4w
+ 3w + 3w
-7 = 7w
/-7 /-7
-1 = w

​Equations do not ALWAYS have just one solution. 

One Solution – The coefficient on sides of the equal sign is different.

 No Solution – Final statement is NOT TRUE.

Many Solutions (Identity) or Infinite Solutions – Final statement is TRUE.

​Equations with 1 solution

7y + 13 = 5y - 3
- 5y - 5y
2y + 13 = -3
-13 -13
2y = -16
/2 /2
y = -8

One Solution

​Equations with no solution

8 + 9p = 9p - 7
- 9p - 9p
8 = -7

This is NOT a true statement, therefore, there is NO Solution!

​Equations with infinitely many solutions

3(7r - 2) = 21r - 6
21r - 6 = 21r - 6
-21r -21r
-6 = -6

This IS a true statement, therefore, there is infinitely Many Solutions!