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lbvjy [14]
3 years ago
12

Explain the difference between properties of equality and properties of inequality when solving equations and inequalities

Mathematics
2 answers:
algol [13]3 years ago
8 0

Answer: An equality is a statement of equal measure. It stands for an absolute statement, without any leeway. That is, there is only a set number of solutions they can take.

Here is an example: x + 17 = 20

In this case, x can only take one solution because it is an absolute statement. Obviously, these can change, but conceptually, they will contain a set of answers a variable can take.

An equality with degree of n will inevitably have n number of answers a variable can take.

However, there are more solutions x can take for an equality. This is because inequality signs are a broader set of equality signs.

Example: x + 17 > 20

In the previous example, there was only one solution that x can take, namely x = 3. However, if we have an inequality, we're merely finding all sets of values x can take that will keep this statement true. In this case, there are an infinite amount of solutions, provided x is greater than 3.

Properties of inequalities vs equalities

This segment is quite tricky to grasp, because we are so used to the equality. The hardest section is to determine when to change the inequality sign. Whenever we multiply or divide by a negative number, we must flip the sign.

Novosadov [1.4K]3 years ago
7 0

Answer:

THE HAMMER

Step-by-step explanation:

I fixed it!

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Which is the equation of a line that passes through the points (1,4) and (-1,1)
horsena [70]

Answer:

The equation of the line is y = 3/2x + 5/2

Step-by-step explanation:

To find the equation of this line, start by using the two points with the slope formula to find the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (4 - 1)/(1 - -1)

m = 3/(1 + 1)

m = 3/2

Now that we have the slope, we can use that and either point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 4 = 3/2(x - 1)

y - 4 = 3/2x - 3/2

y = 3/2x + 5/2

3 0
2 years ago
If one of the roots of the equation x²- 4x + k=0exceeds the other by 2, then find the roots and determine the value of k
BaLLatris [955]

Answer:

roots: 1 and 3

k = 3

Step-by-step explanation:

2 roots: p and p+2

(x-p) (x-p-2) = x² - 4x + k

x² -2px -2x + p² + 2p = x² - 2 (p+1)x + (p² + 2p) = x² -4x + k

-2 (p+1) = -4

p+1 = 2

p = 1   ... root 1

p' = 1+2 = 3   ... root 2

k = p² + 2p = 3

check: (x-1) (x-3) = x² - 4x + 3 = x² - 4x + k

6 0
2 years ago
Each of 11 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating n
Pie

Answer:

The correct answer is 1,51%

Step-by-step explanation:

To get the probability  equally likely of the first 6 examined that have a defective compressor, we use the following formula

P=# of possibilities that meet the condition / #of equally likely possibilities.

As there are multiple events ,  and all must be achieve, we multiply the probabilities.

P1=7 / 11

P2=6 / 10

P3=5 / 9

P4=4 / 8

P5=3 / 7

P6=2 / 6

P(x)=7 / 11*6 / 10*5 / 9*4 / 8*3 / 7*2 / 6=0,01515151515

P(x)=1,51%

3 0
3 years ago
(2x/3)-(5x/9)-(x/6)-(5x/12)=13/2 this equation is equivalent to:
agasfer [191]

Answer:

-17x=234

Step-by-step explanation:

Given that:

\dfrac{2x}{3}-\dfrac{5x}{9}-\dfrac{x}{6}-\dfrac{5x}{12}=\dfrac{13}{2}

\dfrac{72x-60x -18x-45x }{108} = \dfrac{13}{2}

\dfrac{-51x }{108} = \dfrac{13}{2}

-102x =    1404

-\dfrac{102x}{6} = \dfrac{1404}{6}

-17x = 234

6 0
2 years ago
Leila and jo are two of the partners in a business. Leila makes $3 in profits for every $4 that jo makes. If jo makes $60 profit
Aleonysh [2.5K]

Let

x-------> Leila 's profit

y------> Jo's profit

we know that

\frac{x}{y} =\frac{3}{4} ----------> equation 1

For y=\$60

<u>Find the value of x</u>

Substitute the value of y in the equation 1

\frac{x}{60} =\frac{3}{4}

x=60*\frac{3}{4}

x=\$45

therefore

<u>the answer is</u>

Leila make \$45 in profit

5 0
3 years ago
Read 2 more answers
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