In the previous lesson we used the addition property of equality to solve equations. Let’s look at an example.

Click the “Submit” button after entering your answer.

Now, let’s move on with this lesson.

Here we have a scale with three 10-gram weights on the left-hand side, and six 5-gram weights on the right-hand side. Because each side has the same weight, it is perfectly balanced.

Remove weights from both sides of the scale, keeping it balanced.

If one 10-gram weight is removed from the left-hand side, how many 5-gram weights must be removed from the right-hand side in order to keep the scale balanced?

The balanced scale can be represented by the equation: 30 = 30

Removing identical amounts of weight from each side leaves the scale balanced. Likewise, subtracting 5 from both sides both sides of the equation leaves the equality unchanged. We still have a true statement: 20 = 20

This illustrates the subtraction property of equality. If two numbers a and b are equal, then if we subtract the same amount c from each number, the results are also equal.

Notice that subtracting a number from each side is equivalent to adding the negative of that number to each side.

Now, suppose we place an object of unknown weight y and four 1-gram weights on the left-hand side of the scale.

Drag weights to the right-hand side in order to balance the scale.

Which of the following is an equation that represents the balanced scale?

Now, we have an equation representing the balanced scale: y + 4 = 11

Drag weights from both sides to determine the weight y of the object. The goal is to isolate the object on the left-hand side.

What is the value of y?

By removing four 1-gram weights from each side, we have a balanced scale with only the object on the left-hand side.

Similarly, we use the subtraction property of equality to solve for y in our equation. Subtracting 4 from both sides isolates the variable y on the left-hand side, giving us our solution: y = 7

Here we have a table that shows the top five scores of a video game.

Linda Ramirez just finished playing the game. If she had scored 14 points more, her score would equal that of ET.

If x represents Linda’s score, which of the following expressions is equal to ET’s score? Click the “Submit” button after selecting your answer.

The expression, x + 14, is equal to ET’s score. Now, we need to write an equation that can be used to determine the value of x.

Which of the following represents an equation we can use to determine the value of Linda’s score, x? Click the “Submit” button after selecting your answer.

Now, we have an equation for determining Linda’s score.

What is the value of x? Click the “Submit” button after entering your answer.

Adding Linda’s score to the table shows that she ranks fourth among all players.

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