3(q-4)+15=-5(q-7)-10
solve this equation

q = -1

Step-by-step explanation:

Solve for q:

15 - 3 (q - 4) = -5 (q - 7) - 10

-3 (q - 4) = 12 - 3 q:

12 - 3 q + 15 = -5 (q - 7) - 10

Grouping like terms, -3 q + 12 + 15 = (12 + 15) - 3 q:

(12 + 15) - 3 q = -5 (q - 7) - 10

12 + 15 = 27:

27 - 3 q = -5 (q - 7) - 10

-5 (q - 7) = 35 - 5 q:

27 - 3 q = 35 - 5 q - 10

Grouping like terms, -5 q - 10 + 35 = (35 - 10) - 5 q:

27 - 3 q = (35 - 10) - 5 q

35 - 10 = 25:

27 - 3 q = 25 - 5 q

Add 5 q to both sides:

5 q - 3 q + 27 = (5 q - 5 q) + 25

5 q - 5 q = 0:

5 q - 3 q + 27 = 25

5 q - 3 q = 2 q:

2 q + 27 = 25

Subtract 27 from both sides:

2 q + (27 - 27) = 25 - 27

27 - 27 = 0:

2 q = 25 - 27

25 - 27 = -2:

2 q = -2

Divide both sides of 2 q = -2 by 2:

(2 q)/2 = (-2)/2

2/2 = 1:

q = (-2)/2

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

 q = -1

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