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(x+5)/9 +5 = (7x-10)/6

and

(x+5)/10 +5 = (7x-10)/6

Nov 20, 2017
edited by Guest  Nov 20, 2017

#2
+1

Here is the first one:

Solve for x:
(x + 5)/9 + 5 = (7 x - 10)/6

Put each term in (x + 5)/9 + 5 over the common denominator 9: (x + 5)/9 + 5 = 45/9 + (x + 5)/9:
45/9 + (x + 5)/9 = (7 x - 10)/6

45/9 + (x + 5)/9 = ((x + 5) + 45)/9:
(x + 5 + 45)/9 = (7 x - 10)/6

Grouping like terms, x + 5 + 45 = x + (45 + 5):
(x + (45 + 5))/9 = (7 x - 10)/6

45 + 5 = 50:
(x + 50)/9 = (7 x - 10)/6

Multiply both sides by 18:
(18 (x + 50))/9 = (18 (7 x - 10))/6

18/9 = (9×2)/9 = 2:
2 (x + 50) = (18 (7 x - 10))/6

18/6 = (6×3)/6 = 3:
2 (x + 50) = 3 (7 x - 10)

Expand out terms of the left hand side:
2 x + 100 = 3 (7 x - 10)

Expand out terms of the right hand side:
2 x + 100 = 21 x - 30

Subtract 21 x from both sides:
(2 x - 21 x) + 100 = (21 x - 21 x) - 30

2 x - 21 x = -19 x:
-19 x + 100 = (21 x - 21 x) - 30

21 x - 21 x = 0:
100 - 19 x = -30

Subtract 100 from both sides:
(100 - 100) - 19 x = -100 - 30

100 - 100 = 0:
-19 x = -30 - 100

-30 - 100 = -130:
-19 x = -130

Divide both sides of -19 x = -130 by -19:
(-19 x)/(-19) = (-130)/(-19)

(-19)/(-19) = 1:
x = (-130)/(-19)

Multiply numerator and denominator of (-130)/(-19) by -1:
x = 130/19

Here is the second one:

Solve for x:
(x + 5)/10 + 5 = (7 x - 10)/6

Put each term in (x + 5)/10 + 5 over the common denominator 10: (x + 5)/10 + 5 = 50/10 + (x + 5)/10:
50/10 + (x + 5)/10 = (7 x - 10)/6

50/10 + (x + 5)/10 = ((x + 5) + 50)/10:
(x + 5 + 50)/10 = (7 x - 10)/6

Grouping like terms, x + 5 + 50 = x + (50 + 5):
(x + (50 + 5))/10 = (7 x - 10)/6

50 + 5 = 55:
(x + 55)/10 = (7 x - 10)/6

Multiply both sides by 30:
(30 (x + 55))/10 = (30 (7 x - 10))/6

30/10 = (10×3)/10 = 3:
3 (x + 55) = (30 (7 x - 10))/6

30/6 = (6×5)/6 = 5:
3 (x + 55) = 5 (7 x - 10)

Expand out terms of the left hand side:
3 x + 165 = 5 (7 x - 10)

Expand out terms of the right hand side:
3 x + 165 = 35 x - 50

Subtract 35 x from both sides:
(3 x - 35 x) + 165 = (35 x - 35 x) - 50

3 x - 35 x = -32 x:
-32 x + 165 = (35 x - 35 x) - 50

35 x - 35 x = 0:
165 - 32 x = -50

Subtract 165 from both sides:
(165 - 165) - 32 x = -165 - 50

165 - 165 = 0:
-32 x = -50 - 165

-50 - 165 = -215:
-32 x = -215

Divide both sides of -32 x = -215 by -32:
(-32 x)/(-32) = (-215)/(-32)

(-32)/(-32) = 1:
x = (-215)/(-32)

Multiply numerator and denominator of (-215)/(-32) by -1:
x = 215/32

Nov 20, 2017

#1
+1

Step one is simplifying the equatation!

(x+5/9)+5 = (7x-10/6)

x + 5/9 + 5 = 7x − 10/6

x + 5/9 + 5 = 7x + −5/3

x + 50/9 = 7x + −5/3

Step two is subtracting 7x from both sides

−6x + 50/9 −7x = −5/3

Step three is subtracting 50/9 from both sides

−6x = −65/9

Step four is dividing both sides by −6

−6x/−6 =−65/9/−6

x = 65/54

Now the second one! First we simplify the equatation.

x + 1/2 + 5 = 7x + −5/3

x + 11/2 = 7x + −5/3

Step two is to subtract 7x from both sides

−6x + 11/2 = −5/3

Step three is subtracting 11/2 from both sides

(−6x + 11/2 − 11/2 = −5/3 − 11/2)

−6x = −43/6

Now we divide both sides by −6

−6x/−6 = −43/6/−6

x = 43/36

Nov 20, 2017
#2
+1

Here is the first one:

Solve for x:
(x + 5)/9 + 5 = (7 x - 10)/6

Put each term in (x + 5)/9 + 5 over the common denominator 9: (x + 5)/9 + 5 = 45/9 + (x + 5)/9:
45/9 + (x + 5)/9 = (7 x - 10)/6

45/9 + (x + 5)/9 = ((x + 5) + 45)/9:
(x + 5 + 45)/9 = (7 x - 10)/6

Grouping like terms, x + 5 + 45 = x + (45 + 5):
(x + (45 + 5))/9 = (7 x - 10)/6

45 + 5 = 50:
(x + 50)/9 = (7 x - 10)/6

Multiply both sides by 18:
(18 (x + 50))/9 = (18 (7 x - 10))/6

18/9 = (9×2)/9 = 2:
2 (x + 50) = (18 (7 x - 10))/6

18/6 = (6×3)/6 = 3:
2 (x + 50) = 3 (7 x - 10)

Expand out terms of the left hand side:
2 x + 100 = 3 (7 x - 10)

Expand out terms of the right hand side:
2 x + 100 = 21 x - 30

Subtract 21 x from both sides:
(2 x - 21 x) + 100 = (21 x - 21 x) - 30

2 x - 21 x = -19 x:
-19 x + 100 = (21 x - 21 x) - 30

21 x - 21 x = 0:
100 - 19 x = -30

Subtract 100 from both sides:
(100 - 100) - 19 x = -100 - 30

100 - 100 = 0:
-19 x = -30 - 100

-30 - 100 = -130:
-19 x = -130

Divide both sides of -19 x = -130 by -19:
(-19 x)/(-19) = (-130)/(-19)

(-19)/(-19) = 1:
x = (-130)/(-19)

Multiply numerator and denominator of (-130)/(-19) by -1:
x = 130/19

Here is the second one:

Solve for x:
(x + 5)/10 + 5 = (7 x - 10)/6

Put each term in (x + 5)/10 + 5 over the common denominator 10: (x + 5)/10 + 5 = 50/10 + (x + 5)/10:
50/10 + (x + 5)/10 = (7 x - 10)/6

50/10 + (x + 5)/10 = ((x + 5) + 50)/10:
(x + 5 + 50)/10 = (7 x - 10)/6

Grouping like terms, x + 5 + 50 = x + (50 + 5):
(x + (50 + 5))/10 = (7 x - 10)/6

50 + 5 = 55:
(x + 55)/10 = (7 x - 10)/6

Multiply both sides by 30:
(30 (x + 55))/10 = (30 (7 x - 10))/6

30/10 = (10×3)/10 = 3:
3 (x + 55) = (30 (7 x - 10))/6

30/6 = (6×5)/6 = 5:
3 (x + 55) = 5 (7 x - 10)

Expand out terms of the left hand side:
3 x + 165 = 5 (7 x - 10)

Expand out terms of the right hand side:
3 x + 165 = 35 x - 50

Subtract 35 x from both sides:
(3 x - 35 x) + 165 = (35 x - 35 x) - 50

3 x - 35 x = -32 x:
-32 x + 165 = (35 x - 35 x) - 50

35 x - 35 x = 0:
165 - 32 x = -50

Subtract 165 from both sides:
(165 - 165) - 32 x = -165 - 50

165 - 165 = 0:
-32 x = -50 - 165

-50 - 165 = -215:
-32 x = -215

Divide both sides of -32 x = -215 by -32:
(-32 x)/(-32) = (-215)/(-32)

(-32)/(-32) = 1:
x = (-215)/(-32)

Multiply numerator and denominator of (-215)/(-32) by -1:
x = 215/32

Guest Nov 20, 2017
#4
0

(x+5)/10 +5 = (7x-10)/6
(x+55)/10 =(7x -10)/6
6x + 330 =70x - 100
6x-70x =-100 -330
-64x =-430
x =-430/-64
x =215/32

Guest Nov 20, 2017
#3
+1

Here is another presentation for what our guest did. Thanks guest :)

$$\frac{(x+5)}{9} +5 =\frac{ (7x-10)}{6}$$

The lowest common denominator is 18 so multiply every term by 18

That way you will get rid of all the fractions and it will be much easier.

$$\frac{18(x+5)}{9} +18*5 =\frac{18 (7x-10)}{6}\\ \frac{2(x+5)}{1} +90 =\frac{3 (7x-10)}{1}\\ 2(x+5)+90 =3 (7x-10)\\ 2x+10+90 =21x-30\\ 2x+100 =21x-30\\ 130 =19x\\ x=\frac{130}{19}=6\frac{16}{19}$$

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Nov 20, 2017