How To Find A Solution Set

Are you still looking for a unproblematic procedure on how to correspond the solution fix of an inequation on a graph? If aye, then stay on this page. Hither we are giving a detailed step past pace explanation on finding Solution Prepare for Linear Inequations with the solved examples. And then, refer to the post-obit sections and solve the questions easily.

Graphical Representation of the Solution Set of an Inequation

We generally use a number line to stand for the solution set of an inequation on a graph. Following are the steps to represent the solution set of a linear inequation on a graph.

• At first, solve the given linear inequation and detect the solution ready for information technology.
• Mark the solution set on a number line by putting dot.
• If the solution set up is infinite, and then put three more dots to signal infiniteness.

Questions on Finding the Solution Fix of an Inequation and their Representation

Example 1.

Solve the inequation 4x – six < 10, ten ∈ N and correspond the solution gear up graphically?

Solution:

Given linear inequation is 4x – 6 < 10

Add half-dozen to the both sides of inequation

= 4x – half-dozen + half dozen < 10 + 6

= 4x < 16

Divide both sides of the inequation by iv

= 4x/4 < 16/4

= x < iv

So, the replacement set = {1, ii, iii, 4, . . }

Therefore, the solution set up S = {ane, 2, 3} or S = {10 : x ∈ N, x < 4}

Allow us mark the solution set graphically.

The solution set is marked on the number line by dots.

Example 2.

Solve the inequation 8x + 4 > 20, x ∈ W and correspond the solution set graphically?

Solution:

Given linear inequation is 8x + 4 > 20

Subtract 4 from both sides

= 8x + 4 – 4 > twenty – 4

= 8x > 16

Divide both sides by viii

= 8x/viii > xvi/viii

= 10 > 2

Replacement prepare = {0, 1, 2, three, 4, . . . }

Therefore, solution set = {3, 4, v, . . } or Southward = {10 : 10 ∈ W, x > 2}

Permit us mark the solution ready graphically.

The solution set is marked on the number line by dots. Nosotros put three more dots indicate the infiniteness of the solution gear up.

Example 3.

Solve -ii ≥ x ≥ 5, x ∈ I, and represent the solution prepare graphically?

Solution:

Given linear inequation is -2 ≥ x ≥ 5

This has two inequations,

-2 ≥ 10 and 10 ≥ 5

Replacement set = {. . . -three, -ii, -i, 0, one, 2, three . . .}

Solution set for the inequation -2 ≥ x is -ii, -1, 0, i, 2, three, . . i.e S = {-2, -one, 0, ane, ii, 3 . . } = P

And the solution prepare for the inequation 10 ≥ five is 5, 6, 7, 8 . . i.east Q = {v, six, seven, 8 . . .}

Therefore, solution prepare for the given inequation = P ∩ Q

= {5, 6, 7, 8, 9 . . . }

or S = {ten : ten ∈ I, -2 ≥ x ≥ 5}

Let united states of america represent the solution ready graphically.

The solution set is marked on the number line by dots.

Example four.

Solve 0 < 3x – 10 ≤ 12, x ∈ R and represent the solution set up graphically.

Solution:

Given linear inequation is 0 < 3x – 10 ≤ 12

Information technology has two cases.

Instance I:

0 < 3x – ten

Add 10 to both sides

0 + 10 < 3x – 10 + 10

10 < 3x

Divide both sides by three

10/3 < 3x/iii

10/3 < x

Example II:

3x – 10 ≤ 12

Add 10 to both sides

3x – 10 + 10 ≤ 12 + 10

3x ≤ 22

Dissever both sides by iii

3x/x ≤ 22/three

ten ≤ 22/3

S ∩ S' = {three.33 < 10 ≤ seven.33} x ∈ R

= {ten : x ∈ R 3.33 < x ≤ 7.33}

Source: https://ccssmathanswers.com/representation-of-the-solution-set-of-a-linear-inequation/

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