Example 1 :
Solve the following equation and graph the solution on a number line.
9a = 54
9a = 54
Since we are trying to solve for 'a', we have to get rid of '9' which is multiplied by a in the above equation.
To get rid of 9, we have to divide both sides of the equation by 9.
9a/9 = 54/9
a = 6
Example 2 :
Solve the following equation and and graph the solution on a number line.
18 = 6d
Divide both sides by 6.
18/6 = 6d/6
3 = d
Example 3 :
The product of two numbers is 20. If one number is 8, find the other number.
Let x be the other number.
8x = 20
Divide both sides by 8.
8x/8 = 20/8
x = 2.5
The other number is 2.5.
Example 4 :
Three times of x is equal to four times of y. If the value of y is 6, find the value of x.
Given : Three times of x is equal to four times of y.
3x = 4y
Substitute y = 6.
3x = 4(6)
3x = 24
Divide each both sides by 3.
3x/3 = 24/3
x = 8
Example 5 :
Deanna has a recipe for potato cakes that requires 12 eggs to make 3 batches of potato cakes. Represent the given situation as an equation.
Model the equation and find how many eggs are needed per batch.
Write a word equation based on the situation.
Rewrite the equation using a variable for the unknown quantity and the given values for the known quantities.
Let x represent the number of eggs needed per batch.
Then, we have
Therefore, the equation 3x = 12 represents the given situation.
Let us model the equation 3x = 12 using algebra tiles.
To find how many eggs are needed per batch, we have to solve for x.
To solve for x in the above model, we have to isolate x.
There are three x tiles, so draw circles to separate the tiles into 3 equal groups.
One group has been circled here.
In the circled group above, we find one x on the left side and four 1 tiles on the right side.
So, the value of x is 4.
Hence, 4 eggs are needed per batch.
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