Question

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

2x – 7 > 3= ?


`(x)/(4) +11\geq 8`= ?


`-6x+7\geq 19`= ?


-10+4x>50= ?


`(x)/(-2)`-17>-13= ?



`8-2x\leq 46`= ?


`-13x+1\leq -25`= ?


`-7+(x)/(3) \ \textgreater \ -4`= ?


`-9x-19\geq 17`= ?


`16-x\ \textgreater \ 9`= ?

Answer 1

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}`

Explanation:

2x - 7 > 3

2x > 10

x > 5

x/4 + 11 ≥ 8

x/4 ≥ -3

x ≥ -12

-6x + 7 ≥ 19

-6x ≥ 12

x ≤ -2

-10 + 4x > 50

4x > 60

x > 15

-x/2 - 17 > -13

-x/2 > 4

-x > 8

x < -8

8 - 2x ≤ 46

-2x ≤ 38

x ≥ -19

-13x + 1 ≤ -25

-13x ≤ -26

x ≥ 2

-7 + x/3 > -4

x/3 > 3

x > 9

-9x -19 ≥ 17

-9x ≥ 36

x ≤ -4

16 - x > 9

-x > -7

x < 7

Answer 2

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}`

Explanation:

1)
`2x-7 > 3`

Adding 7 to both sides

=> 2x > 3+7

=> 2x > 10

Dividing both sides by 2

=> x > 5

2)
`(x)/(4) + 11 \geq 8`

Subtracting 11 to both sides

`(x)/(4) \geq 8 -11\\(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)
`(x)/(-2) - 17 > -13`

`(x)/(-2) - 17 > -13\\Adding \ 17 \ to \ both \ sides\\\\(x)/(-2) > -13+17\\\\(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 + (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.