Can you solve this?

So firstly, Make this is a single fraction:

After changing it to a single fraction, you should get this:

Then you might say that we cross multiply both sides and find x but you are wrong because in like these type of inequality, we don't cross multiply.

Instead we want to take out the denominator of the fraction:

So we multiply (2x+3)^2 on both sides so the denominator will be eliminated:

Then, you simplify this inequality to:

Then when you solve quadratic equation, you will get: x= -1.5 or x= -1.75 but this quadratic equation is in a inequality so we cannot just leave the answer like that, to answer this 2 values of x in inequality is that:

(x) will be less than the root which is the smallest, (x) will be greater than the root which is greater compared with the roots found in the quadratic inequality.

(x) will be less than -0.75 .==> x< -1.75 ,

(x) will be greater than -1.5.==> x> -1.5

These are the properties that you need to remember at the end while solving any inequality sum.

• Never cross multiply while solving inequalities.
• (x) will be less than the root which is the smallest, (x) will be greater than the root which is greater compared with the roots found in the quadratic inequality.
• Never forget to never get any wrong in inequality sums

Thank you for solving this question D.S.R Manav