7 ( x - 11 ) + 2 = 4 ( x + 3 ) - 1

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Let's simplify both sides of the equation:

7(x-11) + 2 = 4(x+3) - 1
7x - 77 + 2 = 4x + 12 - 1
7x - 75 = 4x + 11

Now, let's isolate the variable x by moving all terms with x to one side of the equation:

7x - 4x = 11 + 75
3x = 86

Finally, let's solve for x:

x = 86/3
x = 28.67

Therefore, the solution to the equation is x = 28.67.