Inequalities with Absolute Values: Understanding inequality

What is the solution to the following inequality?

$10x-4≤-3x-8$

In the exercise, we have an inequality equation.

We treat the inequality as an equation with the sign -=,

And we only refer to it if we need to multiply or divide by 0.

 $10x-4 ≤ -3x-8$

We start by organizing the sections:

$10x+3x-4 ≤ -8$

$13x-4 ≤ -8$

$13x ≤ -4$

Divide by 13 to isolate the X

$x≤-\frac{4}{13}$

Let's look again at the options we were asked about:

Answer A is with different data and therefore was rejected.

Answer C shows a case where X is greater than$-\frac{4}{13}$, although we know it is small, so it is rejected.

Answer D shows a case (according to the white circle) where X is not equal to$-\frac{4}{13}$, and only smaller than it. We know it must be large and equal, so this answer is rejected.

Therefore, answer B is the correct one!

Which diagram represents the solution to the inequality below? 5-8x<7x+3

First, we will move the elements:

5-8x>7x+3

5-3>7x+8x
2>13x

We divide the answer by 13, and we get:

x > \frac{2}{13}

What is the solution to the inequality shown in the diagram?

$3 ≤ x$

Which inequality is represented by the numerical axis below?

-7 < x ≤ 2

Which diagram corresponds to the inequality below?

^{$40x+57≤5x-13≤25x+7$}

What is its solution?

No solution.