Step-by-step explanation:
a). x-5 = -4
⇛x = -5+5
Therefore, x = 0 = 1
b). -8x - 2 = -8
⇛-8x = -8-2
⇛-8x = -10
⇛x = -10÷-8
⇛x = 10/8
Therefore, x = 5/4
c). 3x + 26 = 5x
⇛3x -5x = -26
⇛-2x = -26
⇛x = -26÷-2
⇛x = -26/-3
Therefore, x = 26/3
d). 12 = 4(-17+ 5x)
⇛12 = -68 + 20x
⇛12 +68 = 20x
⇛80 = 20x
⇛x = 20/80
Therefore, x = 1/4
e). x = (3/4)x -2
⇛ x -(3/4)x = -2
Therefore, x = 6
f). 0.5x + 4.75 = 13
⇛0.5x = 13-4.75
⇛0.5x = 8.25
⇛x = 8.25/0.5
Therefore, x = 16.5
g). 127.5 = 12x+(60/8)
⇛127.5 = 12x + (30/4)
⇛-12x = (30/4) - 127.5
⇛-12x = (30/4) - (127.5/1)
⇛-12x = (30*1 - 127.5*4)/4
⇛-12x = (30- 510)/4
⇛-12x = -480/4
⇛-12x = -240/2
⇛-12x = -120
⇛x = -120/-12
Therefore, x = 10
h). (1/7)(-20-4x)=-4
⇛(-20-4x)/7 = -4/1
⇛1(20-4x) =7 (-4)
⇛20 - 4x = -28
⇛-4x = -28-20
⇛-4x = -8
⇛x = -8/-4
Therefore, x = 2
i). -18 = x - 12
⇛-18 + 12 = x
⇛-6 = x
Therefore, x = -6
j). -7(2/3) = 4x-9
⇛-(21+2)/3 = 4x - 9
⇛-(23/3) = 4x -9
⇛-(23/3) + 9 = 4x
⇛-(23/3) + (9/1) = 4x
⇛-(23*1 + 9*3)/3 = 4x
⇛(-23 + 27)/3
⇛(4/3) = 4x
⇛(4/3)÷4 = x
⇛(4/3) × (1/4) = x
⇛(4*1)/(3*4) = x
⇛4/12 = x
Therefore, x = 4/12
l). -6(2.5x + 8) = -123
⇛-15x -48 = -123
⇛-15x = -123+ 48
⇛-15x = -75
⇛x = -75/-15
Therefore, x = 5
m). -19x = 100 + x
⇛-19x - x = 100
⇛-20x = 100
⇛x = 100/-20
Therefore, x = -5
n). 0.2x - 0.5 = 1.2
⇛0.2x = 1.2 + 0.5
⇛0.2x = 1.8
⇛x = 1.8/0.2
Therefore, x = 4
o). (-2)² - 3x = -17
⇛(-2*-2) - 3x = -17
⇛4 - 3x = -17
⇛-3x = -17-4
⇛-3x = -21
⇛x = -21/-3
Therefore, x = 7
p). -(1/2)x -(4/5) = 19/4
⇛-(1/2)x = (19/4) + (4/5)
Take the LCM of the denominator 4 and 5 is 20.
⇛-(1/2)x = (19*5 + 5*4)/20
⇛-(1/2)x = (95 + 16)/20
⇛-(1/2)x =111/20
⇛x = (111/20) + (1/2)
Again take the LCM of the denominator 20 and 2 is 20.
⇛x = (111*1 + 1*10)/20
⇛x = (111 + 10)/20
⇛x = (121/20)
Therefore, x = 121/20
q). (x/8) + 2 = 1/4{(5/16) + 8}
⇛(x/8) + 2 = (5/64) + 2
⇛(x/8) + 2 = (5/64) + (2/1)
Take the LCM of the denominator 1 and 64 is 64 in RHS.
⇛(x/8) +2 = (5*1 + 2*64)/64
⇛(x/8) + 2 = (5 + 128)/64
⇛(x/8) + 2 = 133/64
⇛x/8 = (133/64) - 2
⇛x/8 = (133/64) - (2/1)
Take the LCM of the denominator 1 and 64 is 64 in RHS.
⇛x/8 = (133*1 - 2*64)/64
⇛x/8 = (133 - 128)/64
⇛x/8 = 5/64
On applying cross multiplication, then
⇛x(64) = 8(5)
⇛64x = 40
⇛x = 40/64
⇛x = (40÷4)/(64÷4)
⇛x = 10/12
⇛x = (10÷2)/(16÷2)
Therefore, x = 5/8
r). -6 = -3{(1/7)x + (4/14)}
⇛-6 = -(3/7)x -(6/7)
⇛-6 + (6/7) = -(3/7)x
⇛-(6/1) + (6/7) = -(3/7)x
Take the LCM of the denominator 1 and 7 is 7 in LHS.
⇛(-6*7 + 6*1)/7 = -(3/7)x
⇛(-42 + 6)/7 = -(3/7)x
⇛-(36/7) = -(3/7)x
On applying cross multiplication, then
⇛7(36) = 21x
⇛252 = 21x
⇛252/21= x
⇛12 = x
Therefore, x = 12
s). (1/4)x = 11/4
⇛x = (11/4) - (1/4)
⇛x = (11-1)/4
⇛x = 10/4
⇛(10÷2)/(4÷2)
Therefore, x = 5/2
t). x - (-3) = 9
⇛x + 3 = 9
⇛x = 9-3
Therefore, x = 6.
Please let me know if you have any other questions.
