how would you do this? maths?

Question

6(3x+1) -2(5x-4)<5(x+2)

and

7(3x-4)-(12x -5)>5(2x-3)

and

6(x+4)-7-(3x+10) > 2(4x-5)

the one above '>' has equal to, but dunno how to enter that.

thanks :)

Answer 1

first multiply the (3x+1) by six this would give you

18x+6-2(5x-4)<5(x+2)

Then multiply the (5x-4) by two

18x+6-10x+8<5(x+2)

Multiply the (x+2) by 5

18x+6-10x+8<5x+10

simplify

8x+6+8<5x+10 18x-10x=8x
8x+14<5x+10 6+8=14

Then move all the multiples of x to one side of the <

8x-5x+14<10 Subtract 5x from both sides
3x+14<10 Simplify

Move the other numbers to the other sid of the <

3x<10-14 Subtract 14 from both sides
3x<-4 10-14=-4

x<-4/3 Divide both sides by 3

The others are done the same way. I would sugest you do it on paper untill it becomes natural. It would be much easier in the long run

Answer 2

The original equation:
   6 ( 3x + 1 ) - 2 ( 5x - 4 ) < 5 ( x + 2 )
   18x + 6 - 10x + 8 < 5x + 10
   8x + 14 < 5x + 10
Subtract 5x from both sides:
   3x + 14 < 10
Subtract 14 from both sides:
   3x < -4
Divide both sides by 3
   x < -4/3

The original equation:
   7 ( 3x - 4 ) - ( 12x - 5 ) > 5 ( 2x - 3 )
   21x - 28 - 12x + 5 > 10x - 15
   9x - 23 > 10x - 15
Subtract 10x from both sides:
   -x - 23 > -15
Add 23 to both sides:
   -x > 8
Multiply both sides by -1 and flip the sign:
   x < -8

The original equation:
   6 ( x + 4 ) - 7 - ( 3x + 10 ) > 2 ( 4x - 5 )
   6x + 24 - 7 - 3x - 10 > 8x - 10
   3x + 7 > 8x - 10
Subtract 8x from both sides:
   -5x + 7 > -10
Subtract 7 from both sides:
   -5x > -17
Multiply both sides by -1 and flip the sign:
   5x < 17
Divide both sides by 5:
   x < 17/5

Answer 3

6(3x+1) - 2(5x-4)< 5(x+2)
(18x+6) - (10x +4) < (5x+ 10)
18x - 10x + 6 + 4< 5x + 10
8x + 10 < 5x + 10
8x -5x + 10 < 5x - 5x + 10
3x + 10 < 10
3x + 10 - 10< 10 - 10
3x < 0
3x/3 < 0/3
x < 0

Answer 4

I won't give you the answer to this because it sounds like a homework problem, but I will give you guidance on how to handle it.

The KEY here is knowing something we call the order of operations. It tells you exactly in what order mathematical operations are done.

(1) Anything in parentheses,
(2) Exponents, such as 2 squared (means 2 x 2),
(3) Multiplication and division,
(4) Addition and subtraction.

Using this ordering, now go back and apply it to your problem.

Answer 5

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