Question

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

2x – 7 > 3= ?

$\frac{x}{4} +11\geq 8$= ?

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


-10+4x>50= ?

$\frac{x}{-2}$-17>-13= ?


$8-2x\leq 46$= ?

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

$-7+\frac{x}{3} \ \textgreater \ -4$= ?

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

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

Answer 1

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.

Answer 2

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

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