5(3-x)-2 (4-3x)=11-2 (x-1)

x = 2

Step-by-step explanation:

Solve for x:

5 (3 - x) - 2 (4 - 3 x) = 11 - 2 (x - 1)

5 (3 - x) = 15 - 5 x:

15 - 5 x - 2 (4 - 3 x) = 11 - 2 (x - 1)

-2 (4 - 3 x) = 6 x - 8:

6 x - 8 - 5 x + 15 = 11 - 2 (x - 1)

Grouping like terms, 6 x - 5 x - 8 + 15 = (-5 x + 6 x) + (15 - 8):

(-5 x + 6 x) + (15 - 8) = 11 - 2 (x - 1)

6 x - 5 x = x:

x + (15 - 8) = 11 - 2 (x - 1)

15 - 8 = 7:

x + 7 = 11 - 2 (x - 1)

-2 (x - 1) = 2 - 2 x:

x + 7 = 2 - 2 x + 11

Grouping like terms, -2 x + 2 + 11 = (11 + 2) - 2 x:

x + 7 = (11 + 2) - 2 x

11 + 2 = 13:

x + 7 = 13 - 2 x

Add 2 x to both sides:

2 x + x + 7 = (2 x - 2 x) + 13

2 x - 2 x = 0:

2 x + x + 7 = 13

Grouping like terms, 2 x + x + 7 = (x + 2 x) + 7:

(x + 2 x) + 7 = 13

x + 2 x = 3 x:

3 x + 7 = 13

Subtract 7 from both sides:

3 x + (7 - 7) = 13 - 7

7 - 7 = 0:

3 x = 13 - 7

13 - 7 = 6:

3 x = 6

Divide both sides of 3 x = 6 by 3:

(3 x)/3 = 6/3

3/3 = 1:

x = 6/3

The gcd of 6 and 3 is 3, so 6/3 = (3×2)/(3×1) = 3/3×2 = 2:

x = 2

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