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In this lesson, we will learn how to solve rational equations using cross multiplication.

Q1:

Solve 1 2 5 π₯ + 3 = 5 .

Q2:

Solve 2 π₯ + 1 3 π₯ + 4 = 3 5 .

Q3:

If the average of two numbers is 65, where one of them is 60, find the other number.

Q4:

Find π₯ given π₯ β 2 0 π₯ + 1 0 = 0 .

Q5:

Given that π ( π₯ ) = 7 + π π₯ β 7 1 , π ( π₯ ) = 2 π₯ β 7 2 , and π ( π₯ ) = π ( π₯ ) 1 2 , what is the value of π ?

Q6:

Consider the function π ( π₯ ) = 6 π₯ + 8 π₯ + 1 2 .

For what values of π does π ( π₯ ) = π have a solution?

What is the range of the function π ( π₯ ) ?

Q7:

If 2 π₯ + 7 5 π₯ β 9 = 1 2 , find the value of π₯ .

Q8:

Given that π₯ + π¦ 4 5 = π¦ + π§ 3 3 , which of the following is equal to π₯ β π§ 2 ?

Q9:

Container πΏ has one litre of acid at a 2 5 % concentration, and container π» has the same acid at a 7 5 % concentration. How many litres from π» must be added to πΏ to obtain a 6 7 % concentration?

Q10:

Given that the ratio οΉ π₯ β 8 ο βΆ οΉ 5 π₯ + 6 ο 2 2 is equivalent to 7 βΆ 3 7 , then what are the possible values of π₯ ?

Q11:

If 8 π₯ β 4 π¦ 7 π₯ + π¦ = 1 3 1 6 , find π₯ βΆ π¦ in its simplest form.

Q12:

If the function π ( π₯ ) = π₯ + π₯ π₯ β 1 2 2 , what is the value of π₯ for which the multiplicative inverse of π is 16?

Q13:

Given that π βΆ β β { β 1 } β β , where π ( π₯ ) = π₯ + π π₯ β π and π ( β 5 ) = β 1 4 , determine the values of π and π .

Q14:

Find the solution set of 1 ( π₯ β 1 2 ) = 0 . 0 0 0 1 4 in β .

Q15:

Find the value of π₯ given π₯ + 4 4 π₯ is the multiplicative inverse of 9 1 3 .

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