Question

solution to the inequality 16x−33x<37x+27.

Answer 1

The solution to the inequality is:

$x>\frac{-1}{2}$

Solution:

Given inequality is:

$16x-33x<37x+27$

We have to find the solution to given inequality

$\mathrm{Add\:similar\:elements:}\:16x-33x=-17x$

$-17x<37x+27$

$\mathrm{Subtract\:}37x\mathrm{\:from\:both\:sides}$

$-17x-37x<37x+27-37x$

Simplify the above inequality

$-54x<27$

$\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}$

Remember that, change the inequality sign if you divide or multiply both sides by a negative number

If you divide or multiply both sides by a positive number,the inequality sign will not change

$\left(-54x\right)\left(-1\right)>27\left(-1\right)\\\\54x>-27$

$\mathrm{Divide\:both\:sides\:by\:}54$

$\frac{54x}{54}>\frac{-27}{54}\\\\x>-\frac{1}{2}$

Thus the solution to inequality is found