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Hi!

We have the equation:

$$\frac{17}{36}(1-5)+\frac{2}{36}(25-5)+\frac{17}{36}(x-5)=0$$

(I assume that the x's between the fractions and parentheses are multiplication symbols. However, I recommend that you put dots · , it will be easier not to confuse them with the variable x).

The first step would be to simplify the first two parentheses by doing the math :

$$\frac{17}{36}(-4)+\frac{2}{36}(20)+\frac{17}{36}(x-5)=0$$

Then, you have to do the multiplication :

$$\frac{17\times -4}{36}+\frac{2\times 20}{36}+\frac{17}{36}(x-5)=0$$

$$\frac{-68}{36}+\frac{40}{36}+\frac{17}{36}(x-5)=0$$

Then, we can add the two fractions whose denominator is 36 :

$$\frac{-68+40}{36}+\frac{17}{36}(x-5)=0$$

$$\frac{-28}{36}+\frac{17}{36}(x-5)=0$$

Now, to solve the equation and find the unknown \(x\), we must place the term containing the variable x on one side of the equation, and the constant on the other side. To do this, we'll add \(\frac{28}{36}\) to each side, like this:

$$\frac{-28}{36}+\frac{17}{36}(x-5)+\frac{28}{36}=0+\frac{28}{36}$$

$$\frac{17}{36}(x-5)=\frac{28}{36}$$

This has allowed us to eliminate the term on the left side and move it to the right side.

Our goal is to isolate our variable x. So we'll eliminate the factor \(\frac{17}{36}\), like this:

$$\frac{17}{36}(x-5) \div \frac{17}{36}=\frac{28}{36} \div \frac{17}{36}$$

$$(x-5) =\frac{28}{36} \div \frac{17}{36}$$

To divide fractions, we must reverse the numerator and denominator of the second fraction, then replace the division sign with a multiplication sign:

$$(x-5) =\frac{28}{36} \times \frac{36}{17}$$

$$(x-5) =\frac{28\times 36}{36\times 17} $$

We can eliminate the factor 36 that is in the numerator and denominator :

$$x-5 =\frac{28}{17} $$

Finally, we must eliminate the -5 term by adding it to each side:

$$x-5 +5=\frac{28}{17} +5$$

$$x=\frac{28}{17} +5$$

There you go! Our variable x is now isolated! :) All you have to do now is add and simplify the fraction to have an irreducible fraction.

Here are some worksheets on these concepts that could be useful to you :

• Algebra - Algebraic Expressions | Secondaire | Alloprof
• Solving Equations and Inequalities | Secondaire | Alloprof

I hope this is clearer for you! :)