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.
