How Do You Solve the Equation x/5 - (2x+4)/3 = 1?

  • Thread starter tomtomtom1
  • Start date
I already know the answer is -5.In summary, the conversation discusses solving an equation with algebraic fractions. The steps involved include expanding the fractions and using standard algebra rules to simplify the equation. The final answer is -5.
  • #1
tomtomtom1
160
8
I have been struggling with this question can anyone explain how you would solve this, i have been told the answer is -5 but i want to know how to solve it.

Solve the following equation with algebraic fractions

x/5 - (2x+4)/3 = 1
 
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  • #2
Expand out -(2x+4)/3 and then use your normal rules of algebra. Are you able to expand -(2x+4)/3 ?
 
  • #3
is it 2x/3 + 4/3
 
  • #4
tomtomtom1 said:
is it 2x/3 + 4/3

Right so (2x+5)/3 = 2x/3 + 4/3. If you put this into your equation you will have:

x/5 - (2x/3 +4/3) = 1


Can you simplify the left side of this equation using your standard algebra rules?
 
  • #5
3x/15 - 10x/15 + 4/3

-7x/15 + 4/3 = 1
 
  • #6
tomtomtom1 said:
3x/15 - 10x/15 + 4/3

-7x/15 + 4/3 = 1

For -(2x/3 + 4/3) you are essentially multiplying each term in the bracket by -1. So you should not have +4/3. What should you have instead? After you do that, make -7x/15 the subject of the formula.
 
  • #7
got it

3x/15 - 10x/15 - 4/3 = 1
-7x/15 - 4/3 = 1
-7x/15 = 1 + 4/3
-7x = (1+4/3)*15
-7x = 15+(60/3)
-7x = 35
x = 35/-7
x = -5

Thanks
 

FAQ: How Do You Solve the Equation x/5 - (2x+4)/3 = 1?

What is the first step in solving this equation?

The first step in solving this equation is to combine like terms on the left side of the equation. In this case, we can combine the fractions by finding a common denominator.

How do I find the common denominator?

To find the common denominator, we need to find the lowest number that both 5 and 3 can divide into evenly. In this case, the common denominator is 15.

What do I do after combining the fractions?

After combining the fractions, we need to get rid of any remaining fractions by multiplying both sides of the equation by the common denominator. This will give us a new equation without any fractions.

Is there a specific order I should follow when solving this equation?

Yes, when solving an equation, it is important to follow the order of operations. This means performing addition and subtraction before multiplication and division. In this equation, we should first combine like terms, then multiply both sides by the common denominator, and finally solve for x.

What is the final answer for x?

The final answer for x is 9. After following the steps to solve the equation, we are left with x = 9 as the solution that satisfies the given equation.

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