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Question

Solve each absolute value inequality. Graph the solution
$3 vertical line x vertical line minus 2 less or equal than 10$

hint Hint:

|x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by
$vertical line x vertical line equals open curly brackets table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative x comma x less than 0 end cell row cell x comma x greater or equal than 0 end cell end table close$
First, we simplify the inequality and then solve it by considering the two cases. Then we plot the graph on the x- axis, or the real line R in such a way that the graph satisfies the value of x from both the cases.

The correct answer is: Combining the above two solutions, we get -4 ≤ x ≤ 4

Step by step solution:
The given inequality is
3|x| - 2 ≤ 10
Adding 2 both sides, we get
3|x| ≤ 10 + 2
$not stretchy rightwards double arrow 3 vertical line x vertical line less or equal than 12$
Dividing by 3, we get
|x| ≤ 4
We use the definition of $vertical line x vertical line$ , which is
$vertical line x vertical line equals open curly brackets table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative x comma x less than 0 end cell row cell x comma x greater or equal than 0 end cell end table close$
For $x less than 0$
We have
|x| = - x ≤ 4
Multiplying on both sides, we have
x ≥ - 4
Or
-4 ≤ x
For, x ≥ 0,
We have
|x| = x ≤ 4
That is
x ≤ 4
Combining the above two solutions, we get
$negative 4 less or equal than x less or equal than 4$
We plot the above inequality on the real line.

The points -4 and 4 are included in the graph.

The given inequality contains only one variable. So, the graph is plotted on one dimension, which is the real line. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.

Solve - 0.85t - 0.85t -3.9 = - 8.15

An equation in which highest power of any variable is always 1 is known as a Linear equation.
We will simplify the given equation and find the value of t.

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Solve each absolute value inequality. Graph the solution

The correct answer is: Combining the above two solutions, we get -4 ≤ x ≤ 4

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