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Lady_Fox [76]
3 years ago
10

Write a compound inequality to represent all of the numbers between -4 and 6. Help me please

Mathematics
2 answers:
Nuetrik [128]3 years ago
5 0

Answer:

-4 < x < 6

Step-by-step explanation:

We need to represent all the numbers between -4 and 6, that is -3, -2, -1, 0, 1, 2, 3, 4 and 5.

They are all greater than -4. We generalize it as -4 < x (x is greater than -4).

On the other hand, 6 is greater than all of them, that is x < 6.

As we need to write it as a compound inequality, we just combine the two inequalities we have:

-4 < x < 6 (we write the x just once)

If we want to add the -4 and the 6 in the inequality, we just include them with the appropriate sign:

-4 \leq  x \leq 6

balandron [24]3 years ago
3 0
-4 < n < 6 . . . . . represents all numbers n between -4 and 6 (not inclusive).
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Brainliest for the first solution
mr Goodwill [35]

Q1  Solution:

x = 3 or x = -1

Step-by-step explanation:

x²-2x-3 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -2 and their product -3. By trial and error the two numbers are found to be; -3 and 1. The next step is to split the middle term by substituting it with the above two numbers found;

x²+x-3x-3  =  0

x(x+1)-3(x+1)  = 0

(x-3)(x+1) = 0

Finally we apply the zero Product Property :

If ab = 0 then a  = 0 or b  = 0

This implies;

x-3= 0 or x+1 = 0

x = 3 or x = -1 are the solutions to x²-2x-3 = 0

Q2  Solution:

x  = -1/2 or x  =  3

Step-by-step explanation:

2x²-5x-3  =0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -5 and their product 2(-3)=-6. By trial and error the two numbers are found to be; -6 and 1. The next step is to split the middle term by substituting it with the above two numbers found;

2x²-6x+x-3  = 0

2x(x-3)+1(x-3) = 0

(2x+1)(x-3) = 0

2x+1 = 0 or x-3 =  0

2x = -1 or x =  3

x  = -1/2 or x  =  3 are the solutions of the given quadratic equation.

Q3 Soution:

x = 4 or x = 3

Step-by-step explanation:

x²-7x = -12

x²-7x+12 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -7 and their product 12. By trial and error the two numbers are found to be; -4 and -3. The next step is to split the middle term by substituting it with the above two numbers found;

x²-4x-3x+12 = 0

x(x-4)-3(x-4)  = 0

(x-4)(x-3) = 0

x-4 = 0 or x-3 = 0

x = 4 or x = 3 are the solutions of the given quadratic equation.

Q4:

x = -2/3 or x = 6

Step-by-step explanation:

3x² = 16x+12

3x²-16x-12 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -16 and their product 3(-12)= -36. By trial and error the two numbers are found to be; -18 and 2. The next step is to split the middle term by substituting it with the above two numbers found;

3x²-18x+2x-12 = 0

3x(x-6)+2(x-6) = 0

(3x+2)(x-6) = 0

3x+2 = 0 or x-6 =0

3x = -2 or x = 6

x = -2/3 or x = 6 are the solutions of the given quadratic equation.

Q5:

x = 6 or x = -4

Step-by-step explanation:

x²-2x-24 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -2 and their product -24. By trial and error the two numbers are found to be; -6 and 4. The next step is to split the middle term by substituting it with the above two numbers found;

x²-6x+4x-24 = 0

x(x-6)+4(x-6) = 0

(x-6)(x+4) = 0

x-6 = 0 or x+4 = 0

x = 6 or x = -4 are the solutions to the given quadratic equation.

Q6:

x  = 4/3 or x  = -1

Step-by-step explanation:

3x² = x+4

3x²-x-4 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -1 and their product -12. By trial and error the two numbers are found to be; -4 and 3. The next step is to split the middle term by substituting it with the above two numbers found;

3x²-4x+3x-4 = 0

x(3x-4)+1(3x-4)  =0

(3x-4)(x+1) = 0

3x-4 =0 or x+1 =0

3x  = 4 or x = -1

x  = 4/3 or x  = -1 are the solutions to the given quadratic equation.

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