Solve the Following Inequalities and Represent the Solution on a Number Line: 4 - 2x ≥ 6 - 3x - Mathematics

Solve the following inequalities and represent the solution on a number line:
4 - 2x ≥ 6 - 3x

Sum

We have the inequality
4 - 2x ≥ 6 - 3x
⇒ 3x - 2x ≥ 6 - 4
⇒ x ≥ 2
The graph of the solution set is x ≥ 2.

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Representation of Solution on the Number Line

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Chapter 5: Linear Inequations (Solving Linear Inequations in One Variable) - Exercise

Chapter 5 Linear Inequations (Solving Linear Inequations in One Variable)
Exercise | Q 14.4

Represent the following inequalities on real number line:

3x + 1 ≥ – 5

Represent the following inequalities on real number line:

8 ≥ x > – 3

Use the real number line to find the range of values of x for which:

–1 < x ≤ 6 and –2 ≤ x ≤ 3

Solve the following linear in-equation and graph the solution set on a real number line:

`1/3 (5"x" - 8) >= 1/2 (4"x" - 7) `, x ∈ R

Graph the solution set for each inequality:
x ≥ - 3

Solve the following inequation and graph the solution on the number line.
`-2(2)/(3) ≤ x + (1)/(3) < 3(1)/(3); x ∈ "R"`

Solve the following inequalities and represent the solution set on a number line:
`-3 < - (1)/(2) - (2x)/(3) < (5)/(6), x ∈ "R"`.

Solve the following inequalities and represent the solution set on a number line:
`3 > (2(3 - 4x))/(7) ≥ - 2`.

Solve the inequation : `-2(1)/(2) + 2x ≤ (4x)/(3) ≤ (4)/(3) + 2x, x ∈ "W"`. Graph the solution set on the number line.

If x ∈ R (real numbers) and – 1 < 3 – 2x ≤ 7, find solution set and represent it on a number line.