Which of the following values are solutions to the inequality 6≥4x−5?

Answer:

The solution to the inequality is:

[tex]6\ge \:4x-5\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \frac{11}{4}\:\\ \:\mathrm{Decimal:}&\:x\le \:2.75\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:\frac{11}{4}]\end{bmatrix}[/tex]

-5 and -6 are the solution values.

Step-by-step explanation:

Given the inequality

[tex]6\ge \:4x-5[/tex]

Let us solve the inequality

[tex]6\ge \:4x-5[/tex]

switch sides

[tex]4x-5\le \:6[/tex]

Add 5 to both sides

[tex]4x-5+5\le \:6+5[/tex]

Simplify

[tex]4x\le \:11[/tex]

Divide both sides by 4

[tex]\frac{4x}{4}\le \frac{11}{4}[/tex]

Simplify

[tex]x\le \frac{11}{4}[/tex]

Thus, the solution to the inequality is:

[tex]6\ge \:4x-5\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \frac{11}{4}\:\\ \:\mathrm{Decimal:}&\:x\le \:2.75\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:\frac{11}{4}]\end{bmatrix}[/tex]

In our case, we are given the values -6, 8, and -5

We have already determined that the solution is x ≤ 2.75.

Since the solution is x ≤ 2.75, so -5 and -6 come under the solution set because -5 and -6 are less than 2.75.

Hence, -5 and -6 are the solution values.

The graph of the solution of the inequality is also attached below.

The solutions to the inequality 6 ≥ 4x − 5 is x ≤ 11/4.

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now the given inequality is,

6 ≥ 4x − 5

Adding 5 both the side we get,

6 + 5 ≥ 4x − 5 + 5

⇒ 11 ≥ 4x

Dividing both the side by 4 we get,

11/4 ≥ 4x/4

⇒  11/4 ≥ x

or, x ≤ 11/4

this is the required solution of the given inequality.

Thus, the solutions to the inequality 6 ≥ 4x − 5 is x ≤ 11/4.

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