Welcome to our free-to-use Q&A hub, where students post questions and get help from other students and tutors.

Follow the trail of responses and if you have anything to add please sign up or sign in.

You can ask your own question or look at similar Maths questions.

Your answer is x >=  36/23.

All you have to do is simplify both sides of the equation, then isolate the variable.


I just realised that I misread your question, I thought that 3/4 was a coefficient of the second x, and that you already have a very suitable description of the solution, please refer to Wendy D who has solved your problem

Hi there,

Solving an inequality is almost exactly the same as solving an equality, apart from one crucial thing, if you multiply or divide both sides by a negative number you need to reverse the inequality.

So for your question you want to:

 group all the numbers on the right by adding 7 to both sides.

this leaves the xs on the left, you then want to simplify the xs by bringing them together with the same coefficient, which would be (5 + 3/4) which you can work out. 

It will leave you with some fraction in front of the x, you then want to get the x on its own by multiplying both sides of the inequality by what is on the bottom of the fraction and divide both sides by what is on the top of the fraction.

Non of these things should change the direction of the inequality since you haven't multiplied or divided by a negative number and your inequality should be solved for x.

Hope this helped, get back to me if you have any questions.

it is 52

The denominator may be a negative value and therefore may reverse the inequality. Therefore instead of multiplying through the the denominator you need to multiply by (4x-7) squared.

This  should leave you with:(5x+3)(4x-7)>= 2(4x-7)^2

20x^2-23x-21>=2(16x^2-56x+49)

0>=12x^2 -89x+119

If you then use the formula or complete the square to solve and find the roots of the equation, you should get 7/4 and 17/3.

By drawing a quick sketch of this quadratic, it has a positive value of x squared.and two positive roots so please see the sketch on the whiteboard.

So the solution is


7/4<=x<=17/3


Hello,

lala12345,

I shouldnt have disturbed you but the answers posted below are somewhat wrong.

When we are faced with inequality, we cannot deal it the same way as we deal with equality.

Since 4x-7 can also be negative, so we cant simply multiply it to other side because if we multiply the inequality with negative one, it changes the inequality sign.

rather than multiplying 4x-7 we multiply by (4x-7)^2 to both sides and solve

So

(5x+3)(4x-7)>= 2(4x-7)^2

20X^2-35x+12x-21>= 32x^2 -112x +98

12x^2-89x+119<= 0 

so answer is 

7/4<=x<=17/3


Thanks jack,

I understand how to do it now :)

@lala12345 once you have multiplied by the denominator squared you would multiply out the brackets and have a relatively simply quadratic inequality.

@Liz Herbert multiplying both sides of an inequality is generally not a great idea since it can introduce sign errors. And it appears you have made one. 

@lala12345 Multiplying by the denominator squared is a good idea since a square number is always greater than zero and hence there will not be any sign errors.

Please see attached doc to see how I would approach this problem. I apologise for any mistakes I had to do it in a rush.

Sorry I meant greater than or equal to 2
The question is: (5x+3)/(4x-7) is greater than or equal to zero.And also, you have to multiply by the square of the denominator- not just cancel out the denominator- that's all I know but I can't go on from there...Please, please help!!

Firstly I'm going to assume you mean (5x+3)/(4x-7) ≥ 2.

Doing inequalities is pretty much the same as any other algebra - what you do to one side do to the other. In this case the first thing to do is get rid of the pesky denominator. So multiply both sides by (4x-7):

5x + 3 ≥ 2(4x-7)

Multiply it out just like normal:

5x + 3 ≥ 8x -14

Gather like terms. We want something in the form ......≥ x so we need all the xs on one side and all the numbers on the other. The easiest thing to do is take 5x from each side, which leaves us with: 

3 ≥ 3x -14

Now add 14 to each side:

17≥ 3x

We don't want 3x we just want one x so divide through by 3:

17/3 ≥ x

As a matter of form we usually write inequalities with the x on the left hand side so we need to swap this around. If 17/3 is greater or equal to x that means x is less than or equal to 17/3. So swap sides and reverse the sign. 

 x ≤ 17/3

Job done. 

Are you sure you have typed the question correctly the answers do not come out particularly nice. Also is that 3/4 x or 3/(4x)?

Footer Graphic