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.
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
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
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
Beginning with the equation $x=14$x=14, write the equation produced by subtracting $7$7 from both sides.
Beginning with the equation $x=99$x=99, write the equation produced by dividing both sides by $11$11.
Keep equations balanced by always performing the exact same operation to both sides of the equation.