algebra 2 help?

Question

6: Solve the inequality for x: -5x – 2 ≤ 13
x ≤ -3
x ≥ -3
x ≤ (-11/5)
x ≥ (-11/5)


7: Solve the inequality for x: (4/3)x < 12
x < 16
x > 9
x > 16
x < 9


8: Solve the inequality for x: (2x + 3)/(-3) > 5
x < -9
x > -9
x > 1
x > (-5/2)


9: Solve the inequality for x: -4(x – 3) > 3x + 2
x > (-5/7)
x > (10/7)
x < (10/7)
x < (-5/7)


10: Solve the inequality for x: (2/3)(2x – 4) < (-1/2)(3x + 2)
x > (6/17)
x < (10/17)
x < (6/17)
x > (10/17)

Answer 1

6. Solve the inequality: - 5x - 2 ≤ 13

First: add 2 with both sides (when you move a term to the opposite side, always use the opposite sign).

- 5x - 2 + 2 ≤ 13 + 2
- 5x ≤ 15

Sec: isolate "x" on one side - divide both terms by -5 & when you divide by a term with a negative value, always change the inequality sign in the opposite direction.

- 5x/-5 ≤ 15/-5
x ≥ -3

7. Solve the inequality: (4/3)x < 12

First: eliminate the fraction - multiply the denominator with each term.

(3)(4/3)x < (3)(12)

SEc: cross cancel "like" terms & combine the remaining terms.

4x < 36

Third: isolate "x" - divide both terms by 4.

4x/4 < 36/4
x < 9

P.S. Please complete the rest on your own. Its important for you to try the problems.

Answer 2

6) -5x – 2 ≤ 13
-5x ≤ 15 { add 2 to both sides }
x ≥ -3 { When you mutiply or divide by a negative, you have to reverse the inequality }

7) (4/3)x < 12
x < 12(3/4)
x < 9 { 12/4 = 3; 3*3 = 9 }

8) (2x + 3)/(-3) > 5
2x + 3 < -15 { Remember the multiply by a negative rule above }
2x < -18
x < -9

9) -4(x – 3) > 3x + 2
-4x + 12 > 3x + 2
-7x > -10
7x < 10
x < 10/7

10) (2/3)(2x – 4) < (-1/2)(3x + 2)
4(2x - 4) < -3(3x + 2) { Multiply both sides by 6 to clear the fraction }
8x - 16 < -9x - 6
17x < 10
x < 10/17

Answer 3

6: -5x<= 15 -> x>=-3
7:4x < 36 -> x < 9
8: 2x+3 < -15 -> 2x < -18 -> x<-9
9: -4x +12 > 3x + 2 -> 10 > 7x -> (10 /7) > x
10: (4/3)x - 8/3 < (-3/2)x - 1 -> ( 4/3 + 3/2 )x < 8/3 -1 -> (17/6)x < 5/3 -> x < (10/17)

remember these:
if : m > n -> -m < -n
if : m > n -> m+k > n+k
if : m> n -> km > kn

Answer 4

- 5x - 2 ≤ 13

-5x - 2 + 2 ≤ 13 + 2

- 5x ≤ 15

- 5x/-5 ≥ 15/- 5

x = 15/- 5

x = - 3

- - - - - - - -

4/3)x < 12

3(4/3)x < 3(12)

4x < 36

4x/4 < 36/4

x = 36/4

x = 9

- - - - - - -

(2x + 3)/(- 3) > 5

(-3)[(2x + 3)/(- 3)] < - 3(5)

2x + 3 < - 15

2x + 3 - 3 < - 15 - 3

2x < - 18

2x/2 = - 18/2

x = - 18/2

x = - 9

- - - - - - - - -

- 4(x - 3) > 3x + 2

- 4x + 12 > 3x + 2

- 4x + 12 - 3x > 3x + 2 - 3x

- 7x + 12 > 2

- 7x + 12 - 12 > 2 - 12

- 7x > - 10

- 7x/- 7 < - 10/- 7

x = 10/7

- - - - - - - -

(2/3)(2x - 4 ) < (- 1/2)(3x + 2)

6(2/3)(2x - 4) < - (6)(1/2)(3x + 2)

4(2x - 4)< - 3(3x + 2)

8x - 16 < - 9x - 6

8x - 16 + 9x < - 9x - 6 + 9x

17x - 16 < - 6

17x - 16 + 16 < - 6 + 16

17x < 10

17x/17 < 10/17

x = 10/17

- - - - - - - -s-

Answer 5

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