Keeping Equations Balanced

We want to keep equations balanced so that the two sides of the equals sign remain equivalent. If we don't we could change what the equation means. Think of a balanced set of scales. The scale remains level when the weights on both side of the scales are even. The same thing happens with equations.  

This shows a balanced equation. 

If we add a weight to one side and not to the other, then the scales will no longer be balanced. 

 

Examples

Question 1

Beginning with the equation $x=8$x=8, write the new equation produced by adding 2 to both sides.

Think:

 

 

 

Do: $x+2=10$x+2=10

 

Question 2

Beginning with the equation $x=-99$x=−99, write the new equation produced by dividing both sides by 11.

Think: 

 

 

 

Do: $\frac{x}{11}=-9$x11​=−9

 

Question 3

Beginning with the equation $33x=99$33x=99, write the new equation produced by dividing both sides by 11.

Think: Just like before, we need to divide both the left and right side of the equation by 11.

Do: $3x=9$3x=9

 

Question 4

Beginning with the equation $x=14$x=14, write the equation produced by subtracting $7$7 from both sides. 

 

Question 5

Beginning with the equation $x=99$x=99, write the equation produced by dividing both sides by $11$11.