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3 years ago

What is different between solving inequalities and absolute value inequalities?

Mathematics

2 answers:

notka56 [123]3 years ago

6 0

Answer:

Solving Inequalities are different because in Absolute Value Inequalities the values always have to be positive and in Solving Inequalities doesn't always have to be positive.

Step-by-step explanation:

Ivenika [448]3 years ago

5 0

Answer:

The absolute number of a number a is written as

|a|

And represents the distance between a and 0 on a number line.

An absolute value equation is an equation that contains an absolute value expression. The equation

|x|=a

Has two solutions x = a and x = -a because both numbers are at the distance a from 0.

To solve an absolute value equation as

|x+7|=14

You begin by making it into two separate equations and then solving them separately.

x+7=14

x+7−7=14−7

x=7

x+7=−14

x+7−7=−14−7

x=−21

An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.

The inequality

|x|<2

Represents the distance between x and 0 that is less than 2

Whereas the inequality

|x|>2

Represents the distance between x and 0 that is greater than 2

You can write an absolute value inequality as a compound inequality.

−2<x<2

This holds true for all absolute value inequalities.

|ax+b|<c,wherec>0

=−c<ax+b<c

|ax+b|>c,wherec>0

=ax+b<−corax+b>c

You can replace > above with ≥ and < with ≤.

When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.

Step-by-step explanation:

Hope this helps :)

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Use the substitution method to solve the system of equations

PilotLPTM [1.2K]

You solve the substitution method to solve a system of equality by expressing one variable in terms of the other using one equation, and then plugging this expression in the other(s).

In this case, the first equation gives us a way to express n in terms of m. So, we can replace every occurrence of n in the second equation with the given formula.

The result is

$14m+2n=-8 \iff 14m+2(-7m-4)=-8 \iff 14m-14m-8=-8 \iff -8=-8$

So, the second equation turned to be an equality, i.e. an equation where both sides are the same.

This implies that the system has infinitely many solutions, because every couple $(n,m)$ such that $n=-7m-4$ is a solution to the system, because it satisfies both equations: the first is trivially satisfied, whereas the second is an identity, and as such is satisfied by any value of the variable.

3 0

3 years ago

Which of the fractions shown has the greatest value?

kobusy [5.1K]

Greetings!

The best way to compare fractions is to find the LCM (The Lowest Common Denominator) of each of the fractions. This can be done simply by listing the multiples of the denominators.

Multiples:
3: 3,6,9,12,15,18,21,24,27...210,213
10:10,20,30,40,60,70,80...210,220
6: 6,12,18,24,30,36,42,48...210,216
7: 7,14,21,28,35,42,49...210,217

The LCM is 210:
3*70=210
10*21=210
6*35=210
7*30=210

Now, we must do what we do the denominators to the numerators:
1*70=70
70/210
2*21=42
42/210
1*35=35
=35/210
2*30=60
=60/210

The fraction with the largest numerator has the greatest value; In this case it 1/3 or 70/210.

Hope this helps.
-Benjamin

4 0

3 years ago

Read 2 more answers

Which of the following relations represent a function? A. {(-1,-1),(0,0),(2,2),(5,5)}. B. None of these. C. {(0,3),(0,-3),(-3,0)

Cerrena [4.2K]

Answer:

Step-by-step explanation:

In a list of ordered pairs, a relation that is a function will not have any repeated x-values.

A -- a function (x-values are {-1, 0, 2, 5} with no repeats)

B -- irrelevant

C -- not a function (x-values are {0, 0, -3, 3} with 0 being repeated)

D -- not a function (x-values are {-2, -1, -2, 2} with -2 being repeated)