1) -x - 3 = 7

-x = 7 + 3

-x = 10

x = -10

2) x + 5 = -10

x = -10 - 5

x = -15

3) 2x - 7 = 713

2x = 713 + 7

2x = 720

x = 720 : 2

x = 360

4) -129 - (35 - x) = 55

35 - x = -129 - 55

35 - x = -184

x = 35 - (-184)

x = 219

5) 103 - x = 16 - (13 - 8)

103 - x = 16 - 5

103 - x = 11

x = 103 - 11

x = 192

\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)

\(=\dfrac{1}{182}\)

1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 = 1/182

1/182

...=-15-9=-24

...=4+7=11

...=-12-13=-25

...=13+10=23

...=-4-7=-11

...=-9+13=4

...=12+0=12

...=0-7=-7

...=0+3=3

...=15-17=-2

...=-6

...=-23

...=15-15=0

-15-(+9) = -24

4-(-7) = 11

-12+(-13) = -25

-(-13)-(-10) = 23

-4-(+7) = -11

(-9)-(-13) = 4

-(-12)+0 = 12

0-(+7) = -7

0-(-3) = 3

15-17 = -2

-18+12 = -6

-5-18 = -23

-(-15)+(-15) = 0

-24

11

-25

23

-11

4

12

-7

3

-2

-6

-23

0

(3/8+-3/4+7/12):5/6+1/2
= 5/24:5/6+1/2

= 1/4 + 1/2

=3/4

=5/24 : 5/6 +1/2

=1/4 + 1/2

= 3/4

a) \(2^3.3^2=8.9=72\)

b) \(5^{10}:5^7=5^2=25\)

c) \(2^6:2=2^5=32\)

d) \(7^4:7^4=7^0=1\)

e) \(9^5:9^5=9^0=1\)

a) 23.32=8.9=7223.32=8.9=72

b) 510:57=52=25510:57=52=25

c) 5

32

d) $1$

e) $1$

=2/5(-3/7-5/14)-18/35

=2/5x(-11/14)-18/35

=-22/70-18/35=-29/35

-3/7 . 2/5 + 2/5 . (-5/14) - 18/35

= 2/5 . [ -3/7 + (-5/14) ] - 18/35

= 2/5 . [ -6/14 + (-5/14) ] - 18/35

= 2/5 . -11/14 - 18/35

= -11/35 - 18/35

= -29/35.

\(\dfrac{-3}{7}\cdot\dfrac{2}{5}+\dfrac{2}{5}\cdot\dfrac{-5}{14}-\dfrac{18}{35}=\dfrac{2}{5}\cdot\left(\dfrac{-3}{7}+\dfrac{-5}{14}\right)-\dfrac{18}{35}=\dfrac{2}{5}\cdot\left(-\dfrac{11}{15}\right)-\dfrac{18}{35}=\left(-\dfrac{11}{35}\right)-\dfrac{18}{35}=-\dfrac{29}{35}\)