Solve the following systems of linear in equations:

Question:

Solve the following systems of linear in equations:

$-2<\frac{6-5 x}{4}<7$

Solution:

$-2<\frac{6-5 x}{4}$ and $\frac{6-5 x}{4}<7$

$\frac{6-5 x}{4}>-2$

Multiplying both the sides by 4 in the above equation

$\left(\frac{6-5 x}{4}\right)(4)>-2(4)$

$6-5 x>-8$

Now subtracting 6 from both the sides

$6-5 x-6>-8-6$

$-5 x>-14$

Multiplying both the sides by -1 in above equation

$-5 x(-1)>-14(-1)$

$5 x<14$

Now, dividing both the sides by 5 in above equation

$\frac{5 x}{5}<\frac{14}{5}$

$x<\frac{14}{5}$

Now when

$\frac{6-5 x}{4}<7$

Multiplying both the sides by 4 in the above equation

$\left(\frac{6-5 x}{4}\right)(4)<7(4)$

$6-5 x<28$

Now, subtracting 6 from both sides in above equation

$6-5 x-6<28-6$

$-5 x<22$

Multiplying both the sides by -1 in above equation

$-5 x(-1)<22(-1)$

$5 x>-22$

Dividing both the sides by 5 in above equation

$\frac{5 x}{5}>\frac{-22}{5}$

$x>\frac{-22}{5}$

Therefore,

$x \in\left(\frac{-22}{5}, \frac{14}{5}\right)$