Name: Solution of Inequality
Uploaded: 2019-07-19
Duration: 2 min 35 s
Description: Explore the concept of linear inequalities and solve a linear inequality in one variable algebraically. Learn to represent solutions to a linear inequality o...

Question

Solve the given inequation and represent the solution set on the number line.

4 x - 19 < \frac{3 x}{5} - 2 \leq \frac{- 2}{5} + x, \forall x \in R

Accepted Answer

Given, the inequation $4 x - 19 < \frac{3 x}{5} - 2 \leq \frac{- 2}{5} + x, \forall x \in R$
Solving the inequation $4 x - 19 < \frac{3 x}{5} - 2 \leq \frac{- 2}{5} + x$
Splitting the inequation as $4 x - 19 < \frac{3 x}{5} - 2$ and $\frac{3 x}{5} - 2 \leq \frac{- 2}{5} + x$

Solving $4 x - 19 < \frac{3 x}{5} - 2$

$\Rightarrow \frac{4 x \times 5}{5} - \frac{19 \times 5}{5} < \frac{3 x}{5} - \frac{2 \times 5}{5} \Rightarrow 20 x - 95 < 3 x - 10 \Rightarrow 17 x < 85$

Dividing both the sides by $17$ we get

$x < 5$ ____(i)

Now solving $\frac{3 x}{5} - 2 \leq \frac{- 2}{5} + x$

$\Rightarrow \frac{3 x}{5} - \frac{2 \times 5}{5} \leq \frac{- 2}{5} + \frac{x \times 5}{5} \Rightarrow 3 x - 10 \leq 5 x - 2 \Rightarrow - 2 x \leq 8$

Dividing both sides by $- 2$ , we have

$x \geq - 4$ _____(ii)

From (i) and (ii), We have the range as $- 4 \leq x < 5$

So, the solution set of the inequation is

$\{x : - 4 \leq x < 5, x \in R\}$ or $\{- 4, - 3, - 2 - 1, 0, 1, 2, 3, 4\}$

This solution can be shown on the number line as follows

Hence, the solution is represented above.

Solve the given inequation and represent the solution set on the number line. $4 x - 19 < \frac{3 x}{5} - 2 \leq \frac{- 2}{5} + x, \forall x \in R$

Important Questions on Linear Inequations

Learn and Prepare for any exam you want !

Solve the given inequation and represent the solution set on the number line. 4x-19<3x5-2≤-25+x, ∀ x∈R

Important Questions on Linear Inequations

Learn and Prepare for any exam you want !

Solve the given inequation and represent the solution set on the number line. $4 x - 19 < \frac{3 x}{5} - 2 \leq \frac{- 2}{5} + x, \forall x \in R$