To calculate: The equation 3y+2[5(y−4)−2]=5y+6(7+y)−3

Question

Fachur · Accepted Answer

Calculation:
Consider the given equation,

3 y + 2 [5 (y - 4) - 2] = 5 y + 6 (7 + y) - 3

Now, apply the distributive property:

3 y + 2 [5 (y - 4) - 2] = 5 y + 6 (7 + 9) - 3

3 y + 2 [5 y — 20 - 2] = 5 y + 42 + 6 y — 3

3 y + 10 y — 44 = 5 y + 42 + 6 y — 3

Combine the like terms:

3 y + 10 y — 44 = 5 y + 42 + 6 y — 3

13 y - 44 = 11 y + 39

Now, subtract I ly from both sides:

13 y - 44 = 11 y + 39

13 y — 44 — 11 y = 11 y + 39 + 11 y

Combine the like terms:

13 y — 44 — 11 y = 11 y + 39 + 11 y

2 y - 44 = 39

Add 44 to both sides:

2 y - 44 + 44 = 39 + 44

Combine the like terms:

2 y = 83

Divide both sides by 2:

y = \frac{83}{2}

3 y + 2 [5 (y - 4) — 2] = 5 y + 6 (7 + 9) - 3

.

3 y + 2 [5 (y - 4) - 2] = 5 y + 6 (7 + y) - 3

3 (\frac{83}{2}) + 2 [5 (\frac{83}{2} - 4) - 2] \overset{?}{=} 5 (\frac{83}{2}) + 6 (7 + \frac{83}{2}) - 3

(\frac{249}{2}) + 2 [(\frac{415}{2} - 20) - 2] \overset{?}{=} (\frac{415}{2}) + (42 + \frac{498}{2}) - 3

(\frac{249}{2}) + [\frac{830}{2} - 40 - 4] \overset{?}{=} (\frac{415}{2}) + 42 + \frac{498}{2} - 3

On further solution:

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To calculate: The equation 3y+2\left[5\left(y-4\right)-2\right]=5y+