Question

Which equation has the same solution as 4-2(x-5)=x-19

(A) 2(x+5)= -8.
(B) 3(x-3)=9
(C) x+2=2x-3
(D) 3x-4=2x+7

Answer 1

Answer:3x-4=2x+7

Explanation:

first, 4-2x+10=x-19

14+19 =x+2x

33=3x

x=11

A. 2x+10=8

2x= -18

x=-9

B. 3x-9=9

3x=18

x=6

C. x+2=2x-3

3x = 5

x = 5/3

D. 3x-4 = 2x+7

3x-2x=7+4

x=11

Answer 2

3x-4=2x+7 thus: (D)

x = 11

Explanation:

Solve for x:

3 x - 4 = 2 x + 7

Subtract 2 x from both sides:

(3 x - 2 x) - 4 = (2 x - 2 x) + 7

3 x - 2 x = x:

x - 4 = (2 x - 2 x) + 7

2 x - 2 x = 0:

x - 4 = 7

Add 4 to both sides:

x + (4 - 4) = 4 + 7

4 - 4 = 0:

x = 7 + 4

7 + 4 = 11:

Answer: x = 11

___________________________

Solve for x:

4 - 2 (x - 5) = x - 19

-2 (x - 5) = -2 x + 10:

(-2 x + 10) + 4 = x - 19

Add like terms. 4 + 10 = 14:

-2 x + 14 = x - 19

Subtract x from both sides:

(-2 x - x) + 14 = (x - x) - 19

-2 x - x = -3 x:

-3 x + 14 = (x - x) - 19

x - x = 0:

-3 x + 14 = -19

Subtract 14 from both sides:

(14 - 14) - 3 x = -14 - 19

14 - 14 = 0:

-3 x = -14 - 19

-14 - 19 = -33:

-3 x = -33

Divide both sides of -3 x = -33 by -3:

(-3 x)/(-3) = (-33)/(-3)

(-3)/(-3) = 1:

x = (-33)/(-3)

The gcd of -33 and -3 is -3, so (-33)/(-3) = (-3×11)/(-3×1) = (-3)/(-3)×11 = 11:

Answer: x = 11