Question

Solution set of the inequation given by -11≤4x-3≤13 is​

Answer 1

Given :  inequation given by -11≤4x-3≤13

To Find : Solution set

Solution:

-11 ≤ 4x-3 ≤ 13

Adding 3 in each

=> -11 + 3  ≤ 4x-3 + 3  ≤ 13  + 3

=> - 8  ≤ 4x  ≤ 16

Dividing by 4 each

=> - 2   ≤ x  ≤  4

x ∈ [ -2 , 4]

Solution set     is x ∈ [ -2 , 4]

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Answer 2

Step-by-step explanation:

Given:

$- 11 \leqslant 4x - 3 \leqslant 13$

To find: Solution set of inequation.

Solution:

Let us take LHS first

$- 11 \leqslant 4x - 3$

Add 3 both sides

$- 11 + 3 \leqslant 4x - 3 + 3 \\ \\ - 8 \leqslant 4x$

divide both sides by 4

$\frac{ - 8}{4} \leqslant \frac{4x}{4} \\ \\ \bold{- 2 \leqslant x}...ineq1$

Now take RHS

$4x - 3 \leqslant 13$

add 3 both sides

$4x - 3 + 3 \leqslant 13 + 3 \\ \\ 4x \leqslant 16$

divide both sides by 4

$\frac{4x}{4} \leqslant \frac{16}{4} \\ \\ \bold{x \leqslant 4}...ineq2$

Combine both ineqs

$- 2 \leqslant x \leqslant 4$

or

$x \in [-2,4]$

Final answer:

Solution set of inequation is

$\bold{\red{x \in [-2,4]}}$

Hope it helps you.

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