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Vikentia [17]
3 years ago
8

Please solve each inequality and show you work thank you so much:)

Mathematics
2 answers:
KIM [24]3 years ago
8 0

Answers:

\boxed{x > 5}\\ \boxed{x \geq  -12}\\\boxed{x \leq  -2}\\\boxed{x > 15}\\\boxed{x < -8}\\\boxed{x \geq  -19}\\ \boxed{x \geq  2}\\\boxed{x > 9}\\\boxed{ x \leq  -4}\\ \boxed{x < 7}

Step-by-step explanation:

2x - 7 > 3

2x > 10

<u>x > 5</u>

x/4 + 11 ≥ 8

x/4 ≥ -3

<u>x ≥ -12</u>

-6x + 7 ≥ 19

-6x ≥ 12

<u>x ≤ -2</u>

-10 + 4x > 50

4x > 60

<u>x > 15</u>

-x/2 - 17 > -13

-x/2 > 4

-x > 8

<u>x < -8</u>

8 - 2x ≤ 46

-2x ≤ 38

<u>x ≥ -19</u>

-13x + 1 ≤ -25

-13x ≤ -26

<u>x ≥ 2</u>

-7 + x/3 > -4

x/3 > 3

<u>x > 9</u>

-9x -19 ≥ 17

-9x ≥ 36

<u>x ≤ -4</u>

16 - x > 9

-x > -7

<u>x < 7</u>

andrey2020 [161]3 years ago
6 0

Answer:

1) \boxed{x > 5}

2) \boxed{x \geq  -12}

3) \boxed{x \leq  -2}

4) \boxed{x > 15}

5) \boxed{x < -8}

6) \boxed{x \geq  -19}

7) \boxed{x \geq  2}

8) \boxed{x > 9}

9) \boxed{ x \leq - 4}

10) \boxed{x < 7}

Step-by-step explanation:

1) 2x-7 > 3

Adding 7 to both sides

=> 2x > 3+7

=> 2x > 10

Dividing both sides by 2

=> x > 5

2) \frac{x}{4} + 11 \geq 8

Subtracting 11 to both sides

\frac{x}{4} \geq 8 -11\\\frac{x}{4}\geq  -3

Multiplying both sides by 4

x ≥ -3 * 4

x ≥ -12

3) -6x+7 ≥ 19

Subtracting 19 to both sides

=> -6x ≥ 19-7

=> -6x ≥ 12

Dividing both sides by -6

=> x ≤ -2

4) -10 + 4x > 50

Adding 10 to b.s

=> 4x > 50+10

=> 4x > 60

Dividing b.s by 4

=> x > 15

5) \frac{x}{-2} - 17 > -13

\frac{x}{-2} - 17 > -13\\Adding \ 17 \ to \ both \ sides\\\\\frac{x}{-2} > -13+17\\\\\frac{x}{-2} > 4\\Multiplying both sides by -2

=> x < 4*-2

=> x < -8

6) 8 - 2x ≤ 46

Subtracting 8 from b.s

=> -2x ≤ 46-8

=> -2x ≤ 38

Dividing b.s by -2

=> x ≥ -19

7) -13x+1 ≤ -25

Subtracting 1 from both sides

=> -13x ≤ -25-1

=> -13x ≤ -26

Dividing both sides by -13

=> x ≥ 2

8) -7 + \frac{x}{3} > -4

Adding 7 to b.s

=> x/3 > -4+7

=> x/3 > 3

Multiplying 3 to b.s

=> x > 3*3

=> x > 9

9) -9x-19 ≥ 17

Adding 19 to both sides

=> -9x ≥ 17+19

=> -9x ≥ 36

Dividing both sides by -9

=> x ≤ -4

10) 16 - x > 9

Adding x to both sides

=> 16 > 9 + x

Subtracting 9 from both sides

=> 16 - 9 > x

=> 7 > x

OR

=> x < 7

NOTE: Whenever, we divide the inequality by a negative signed term, the inequality changes to its opposite.

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<h3>What is a factor?</h3>

A factor is a number that completely divides another number.

In other words, since the result may be divided by the two whole numbers we are multiplying, they are factors of the result if multiplying two whole numbers produces a result.

The numbers that can divide a number exactly are called factors.

There is none left over after division as a result.

The numbers you multiply together to produce another number are called factors.

A factor is hence the division of another number.

So, we have the expression: x³-5x²-2x+24

Now, calculate the factors as follows:

x³-5x²-2x+24

We already know that: P(-2) = 0

Hence, x+2 is a factor.

Now, other factors are: x² - 7x + 12

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Therefore, the factors of the expression x³-5x²-2x+24 are: (x+2)(x-3)(x-4)

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Correct question:
What is the factor of x³-5x²-2x+24?

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<h3>How to determine the effect of a</h3>

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An exponential function of the above form is represented as:

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See attachment for the graph of the four functions.

<u>When a is large</u>

This is represented by y = 14\sqrt{x

In this case, the curve of the base form y = \sqrt x is vertically stretched and it moves closer to the y-axis

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This is represented by y = 5\sqrt x

In this case, the curve of the base form y = \sqrt x is vertically stretched and it moves away from the x-axis

<u>When a is negative</u>

This is represented by y = -2\sqrt{x

In this case, the curve of the base form y = \sqrt x is vertically stretched and is reflected across the y-axis.

Read more about function transformation at:

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