Question

A) 6(x-1)=9.4-1.7x

b) 3.5-9a=2(0.5a-4)
c) 0.2(5x-6)+2x=0.8
d) -3(y+2.5)=6.9-4.2y

a) x = 1.6
b) a = -0.2
c) x = 2
d) y = -2.1

Answer 1

a) The solution to the equation A) is x = 1.6.

b) The value of a is -0.2.

c) The value of x is 2.

d) The value of y is -2.1.

Explaination:

A) To find the value of x, we isolate x in the expression 6x - 6 = 9.4 + 1.7x. This results in the quadratic equation x^2 - 1.7x - 3.4 = 0, which can be solved using the quadratic formula (x = (-b ± sqrt(b^2 - 4ac)) / 2a). The value of x obtained is approximately 1.6.

B) To find the value of a, we isolate a in the expression 3.5 - 9a = 2(0.5a - 4). This results in the quadratic equation a^2 + a + 0.8 = 0, which can be solved using the quadratic formula (a = (-b ± sqrt(b^2 - 4ac)) / 2a). The value of a obtained is approximately -0.2.

C) To find the value of x, we isolate x in the expression 0.2(5x - 6) + 2x = 0.8. This results in the linear equation -9x + 12 = -16, which can be solved by finding the value of x that satisfies this equation (x = (12 + 16) / (-9)) = approximately 2. D) To find the value of y, we isolate y in the expression -3(y + 2.5) = 6.9 - 4.2y. This results in the quadratic equation y^2 + (8/3)y + (69/12) = 0, which can be solved using the quadratic formula (y = (-b ± sqrt(b^2 - 4ac)) / 2a). The value of y obtained is approximately -2.1.