Solve the equation and check the solution:?

Question

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

Answer 1

7 - [2(3x + 4) - 5] = x - 3
7 - [6x + 8 - 5] = x - 3
7 - [6x + 3] = x - 3
7 - 6x - 3 = x - 3
4 - 6x = x - 3
4 - 7x = -3
-7x = -7
x = 1
Check:
7 - [2(3*1 + 4) - 5] = 1 - 3
7 - [(2(3+4) - 5] = -2
7 - [2(7)-5] = -2
7 - [14-5] = -2
7 - 9 = -2
-2 = -2

Answer 2

Simplifying
7 + -1[2(3x + 4) + -5] = x + -3

Reorder the terms:
7 + -1[2(4 + 3x) + -5] = x + -3
7 + -1[(4 * 2 + 3x * 2) + -5] = x + -3
7 + -1[(8 + 6x) + -5] = x + -3

Reorder the terms:
7 + -1[8 + -5 + 6x] = x + -3

Combine like terms: 8 + -5 = 3
7 + -1[3 + 6x] = x + -3
7 + [3 * -1 + 6x * -1] = x + -3
7 + [-3 + -6x] = x + -3

Combine like terms: 7 + -3 = 4
4 + -6x = x + -3

Reorder the terms:
4 + -6x = -3 + x

Solving
4 + -6x = -3 + x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.
4 + -6x + -1x = -3 + x + -1x

Combine like terms: -6x + -1x = -7x
4 + -7x = -3 + x + -1x

Combine like terms: x + -1x = 0
4 + -7x = -3 + 0
4 + -7x = -3

Add '-4' to each side of the equation.
4 + -4 + -7x = -3 + -4

Combine like terms: 4 + -4 = 0
0 + -7x = -3 + -4
-7x = -3 + -4

Combine like terms: -3 + -4 = -7
-7x = -7

Divide each side by '-7'.
x = 1

Simplifying
x = 1

Answer 3

7 - [2(3x + 4) - 5] = x - 3
7 - 6x - 8 + 5 = x - 3
-6x - x = -3 - 7 + 8 - 5
-7x = -7
x = 1

Check:
7 - [2(3(1) + 4) - 5] = 1 - 3
7 - (2(7) - 5) = -2
7 - (14 - 5) = -2
7 - 9 = -2
-2 = -2 (proven)