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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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