Solving Equations by Adding or Subtracting the Same Number from Both Sides

🏆Practice solution of an equation by adding/subtracting two sides

This method allows us to add or subtract the same element from both sides of the equation without changing the final result, that is, the outcome of the equation will not be affected by the fact that we have added or subtracted the same element from both sides.

Let's see what the logic of this method is:

José and Isabel, for example, are twin siblings who receive their weekly allowance for the first time.

José and Isabel receive 10 10 euros each, so at this moment they have exactly 10 10 euros per person.

After a month, each has received another 2 2 euros, so now each has 12 12 euros.

We see that adding 2 2 euros to the amount each of them had has not affected the equivalence between them: both still have the same amount of money.

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\( 11=a-16 \)

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Below, we provide you with some examples where we apply this method.

Example 1

X+5+2=3 X+5+2=3

If we are asked what the value of the expression X+5 X+5 is, we can leave it on the left side of the equation if we subtract the number 2 2 from both sides.

X+5+2=3 X+5+2=3   / 2 -2

X+5=1 X+5=1

Here we see that the expression X+5 X+5 is equivalent to 1 1 .


Example 2

X+74=10 X+7-4=10

If we are asked what the value of the expression X+7 X+7 is, we can leave it on the left side of the equation if we add the number 4 4 to both sides of the equation.

X+74=10 X+7-4=10 / +4 +4

X+7=14 X+7=14

Here we see that the expression X+7 X+7 is equivalent to 14 14 .



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