The distance between two real numbers $x,y$ is the absolute value of their difference, $|x-y|$ . So the statement "all $x$ that are 1/4 away from -6" is captured in the equation

$|x-(-6)|=\dfrac14$

$|x+6|=\dfrac14$

To solve, you can use the definition of absolute value: if $x$ is not negative, then $|x|=x$ ; otherwise, $|x|=-x$ .

So there are two cases to consider:

1. Suppose $x+6\ge0$ . Then $|x+6|=x+6$ , and the equation reduces to

$x+6=\dfrac14\implies x=-\dfrac{23}4$

2. Suppose $x+6$ . Then $|x+6|=-(x+6)=-x-6$ and

$-x-6=\dfrac14\implies x=-\dfrac{25}4$

$-6=-\dfrac{24}4$ , so the two solutions we found are correct because both $-\dfrac{23}4$ and $-\dfrac{25}4$ are indeed 1/4 away from -6.

- - -

For the question regarding inequality, you know that the absolute value must return a non-negative number. In other words, there is no $x$ such that $|x|$ .

6 0

2 years ago

The figure above shows a right-angled triangle OAB. AOC is a minor sector enclosed in the triangle. If OA = 7 cm, AB = 6 cm, cal

nataly862011 [7]

Answer:

La respuesta es 7+6 ó 6+7 que es 13

3 0

3 years ago

Quadrilaterals ABCD and EFGH are similar. If the perimeter of the quadrilateral ABCD is equal to 4y² what is the perimeter of th

UNO [17]

Answer:

Can't be determined.

Step-by-step explanation:

From the fact that the quadrilaterals are similar:

Corresponding sides are in proportion and

Corresponding angles are congruent.

We can't create a proportion, so there's nothing else that we can determine.

4 0

2 years ago

Read 2 more answers

What is the height, h, of the large triangle? Area of triangle = 108

gladu [14]

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A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangleA) an equilateral triangle
A) an equilateral triangleA) an equilateral triangle
A) an equilateral triangleA) an equilateral triangleA) an equilateral triangle
A) an equilateral triangleA) an equilateral triangle
A) an equilateral triangleA) an equilateral triangle
A) an equilateral triangle
A) an equilateral triangleA) an equilateral triangle
A) an equilateral triangle

4 0

3 years ago