Question

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

Answer 1

Answer:

The answer of the question is this:

Answer 2

Answer:

The solution to the inequality is:

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

-5 and -6 are the solution values.

Step-by-step explanation:

Given the inequality

$6\ge \:4x-5$

Let us solve the inequality

$6\ge \:4x-5$

switch sides

$4x-5\le \:6$

Add 5 to both sides

$4x-5+5\le \:6+5$

Simplify

$4x\le \:11$

Divide both sides by 4

$\frac{4x}{4}\le \frac{11}{4}$

Simplify

$x\le \frac{11}{4}$

Thus, the solution to the inequality is:

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

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.