Equations and Inequalities - Math 9?

Question

Please solve and explain in detail:

1) 0.625x + 0.75 = 7
2) 2/3 x - 3 3/4 = 11
3) x/6 = 7/8

Answer 1

1. .625x + .75 = 7

tranpose .75:
.625 x = 7 minus .75
.625 x = 6.25

then tranpose .625 too

x = 6.25 divided by .625
x = 10

2. 2/3x - 3 3/4 =11

transpose 3 3/4:
2/3x = 11 plus 3 3/4
2/3 x = 14 3/4

then, transpose 2/3:
x = 14 3/4 divided by 2/3
x = 22 1/8

3.x/6 = 7/8

transpose 1/6 to the other side of the equation:
x = 7/8 multiplied by 1/6
x = 7/48

hope that helped! :))

Answer 2

1) 0.625x + 0.75 = 7
subtract 0.75 from each side of the equation
0.625x = 6.25
now divide each side of the equation by 0.625
x = 10

2) 2/3 x - 3 3/4 = 11
add 3 3/4 to each side of the equation
2x/3 = 7 1/4 or 2x/3 = 29/4
now you need to use cross multiplication
2x(4) = 3(29)
8x = 87
now divide 87 by 8
x = 10 7/8 or 87/8

3) x/6 = 7/8
use cross multiplication
x(8) = 6(7)
8x = 42
divide 42 by 8
x = 5.25 or x = 21/4

hope that helps

Answer 3

1) 0.625x+0.75=7
=>0.625x=7-0.75
=> 0.625x=6.25
=>x=6.25/0.625=10 ans
2)2/3 x-3 3/4=11
=> 2x/3-15/4=11
=>2x/3=11-15/4=29/4
=>8x=87 [by cross-multiplication]
=>x=87/8=10 7/8
3)x/6=7/8
=>8x=42 [by cross-multiplication]
=>x=42/8=5 1/4

Answer 4

portion of the rectangle is: x(x-3) = 10 x^2 -3x -10 =0 Discriminant D = (-3)^2 -4(-10)(one million) = 9 +40 =40 9 = 7^2 x1 = (3 -7)/2 = -2 x2 = (3 +7)/2 = 5 length = x -3 and width = x the width can't be damaging (x = -2 is rejected) in basic terms answer is x = 5 length = x -3 = 5-3 =2 width = 5

Answer 5

Question 1
0.625x = 6.25
x = 6.25 / 0.625
x = 10

Question 2
(2/3).x - 15 / 4 = 11
8x - 45 = 132
8x = 177
x = 177 / 8

Question 3
x = 42 / 8
x = 21 / 4