Question

7y/6=5/9 3+z/8=6/11 2x+1/3=1/2 343:a=98:60 7:8=x= 96 2/x=27/108

Answer 1

7y/6=5/9
7у*9=6*5
63у=30
у=30/63

3+z/8=6/11
z/8=6/11-33/11
z/8=-27/11
11z=-27*8
11z=-216
z=-216/11

2x+1/3=1/2
2x=3/6-2/6
2x=1/6
x=1/12

343:a=98:60
98a=343*60
98a=20580
a=20580/98
a=210

7:8=x:96
8х=96*7
8х=672
х=84

2/x=27/108
27х=108*2
27х=216
х=8

Answer 2

7y/6=5/9
7у*9=6*5
63у=30
у=30/63

3+z/8=6/11
z/8=6/11-33/11
z/8=-27/11
11z=-27*8
11z=-216
z=-216/11

2x+1/3=1/2
2x=3/6-2/6
2x=1/6
x=1/12

343:a=98:60
98a=343*60
98a=20580
a=20580/98
a=210

7:8=x:96
8х=96*7
8х=672
х=84

2/x=27/108
27х=108*2
27х=216
х=8

Answer 3

To solve the given equation, let's break it down step by step:

Step 1: Simplify the equation 7y/6 = 5/9 + 3 + z/8 To add fractions, we need a common denominator. The common denominator for 9 and 8 is 72.

7y/6 = 5/9 + 3 + z/8 Multiply the numerator and denominator of 5/9 by 8: (5/9) * (8/8) = 40/72 Multiply the numerator and denominator of 3 by 72/72: (3) * (72/72) = 216/72 Multiply the numerator and denominator of z/8 by 9: (z/8) * (9/9) = 9z/72

So, the equation becomes: 7y/6 = 40/72 + 216/72 + 9z/72

Now, we can combine the fractions on the right side of the equation: 7y/6 = (40 + 216 + 9z)/72

Step 2: Simplify the equation 3 + z/8 = 6/11 + 2x To add fractions, we need a common denominator. The common denominator for 8 and 11 is 88.

3 + z/8 = 6/11 + 2x Multiply the numerator and denominator of 6/11 by 8: (6/11) * (8/8) = 48/88 Multiply the numerator and denominator of 3 by 88/88: (3) * (88/88) = 264/88

So, the equation becomes: 264/88 + z/8 = 48/88 + 2x

Now, we can combine the fractions on the left side of the equation: (264 + z)/88 = (48 + 2x)/88

Step 3: Simplify the equation 1/2 + 343:a = 98:60 + 7:8 To divide fractions, we multiply by the reciprocal of the second fraction.

1/2 + 343:a = 98:60 + 7:8 Divide 343 by a: 343/a Divide 98 by 60: (98/60) * (5/5) = 490/300 Divide 7 by 8: 7/8

So, the equation becomes: 1/2 + 343/a = 490/300 + 7/8

To add fractions, we need a common denominator. The common denominator for 2 and 300 is 600.

1/2 + 343/a = (490 + (300 * 7))/300 + 7/8 1/2 + 343/a = (490 + 2100)/300 + 7/8 1/2 + 343/a = 2590/300 + 7/8

Now, we can combine the fractions on the right side of the equation: 1/2 + 343/a = (2590 + (300 * 7))/300 + 7/8 1/2 + 343/a = (2590 + 2100)/300 + 7/8 1/2 + 343/a = 4690/300 + 7/8

Step 4: Simplify the equation 98:60 + 7:8 = x = 96 + 2/x = 27/108 To divide fractions, we multiply by the reciprocal of the second fraction.

98:60 + 7:8 = x = 96 + 2/x = 27/108 Divide 98 by 60: (98/60) * (5/5) = 490/300 Divide 7 by 8: 7/8 Divide 27 by 108: 27/108

So, the equation becomes: 490/300 + 7/8 = x = 96 + 2/x = 27/108

To add fractions, we need a common denominator. The common denominator for 300 and 8 is 2400.

490/300 + 7/8 = (490 * 8)/(300 * 8) + (7 * 300)/(8 * 300) 490/300 + 7/8 = 3920/2400 + 2100/2400

Now, we can combine the fractions on the left side of the equation: (3920 + 2100)/2400 = x = 96 + 2/x = 27/108 6020/2400 = x = 96 + 2/x = 27/108

Step 5: Solve for x Let's solve the equation 6020/2400 = 96 + 2/x = 27/108 for x.

6020/2400 = 96 + 2/x = 27/108

To simplify, we can divide both sides of the equation by 20:

301/120 = 96 + 2/x = 27/108

Now, let's solve for x by isolating it on one side of the equation:

301/120 - 96 = 2/x - 27/108

To add fractions, we need a common denominator. The common denominator for 120 and 108 is 1080.

(301 * 9)/(120 * 9) - (96 * 9)/108 = (2 * 1080)/(x * 1080) - (27 * 10)/(108 * 10)

2709/1080 - 864/1080 = 2160/1080x - 270/1080

Now, we can combine the fractions on the left side of the equation:

(2709 - 864)/1080 = (2160 - 270)/1080x

1845/1080 = 1890/1080x

To solve for x, we can cross-multiply:

1845 * 1080x = 1890 * 1080

1992600x = 2041200

Now, divide both sides of the equation by 1992600 to solve for x:

x = 2041200 / 1992600

Simplifying the fraction gives us:

x = 1.025

So, the solution to the given equation is x = 1.025.

I hope this helps! Let me know if you have any further questions.