%2B(x%2B3)%2B(x-2)%2B3(x%2B3)-1%3D87.jpeg "(x)+(x+3)+(x-2)+3(x+3)-1=87")
Solving the Equation: (x) + (x + 3) + (x - 2) + 3(x + 3) - 1 = 87
This article will guide you through the steps to solve the equation (x) + (x + 3) + (x - 2) + 3(x + 3) - 1 = 87. Let's break down the process:
Step 1: Simplify the Equation
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Distribute: Multiply the 3 by the terms inside the parentheses: (x) + (x + 3) + (x - 2) + 3x + 9 - 1 = 87
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Combine like terms: Add all the 'x' terms together and all the constant terms together: x + x + x + 3x + 3 - 2 + 9 - 1 = 87 6x + 9 = 87
Step 2: Isolate the Variable
- Subtract 9 from both sides: 6x + 9 - 9 = 87 - 9 6x = 78
Step 3: Solve for x
- Divide both sides by 6: 6x / 6 = 78 / 6 x = 13
Solution
Therefore, the solution to the equation (x) + (x + 3) + (x - 2) + 3(x + 3) - 1 = 87 is x = 13.
Verification
To verify our solution, we can substitute x = 13 back into the original equation:
(13) + (13 + 3) + (13 - 2) + 3(13 + 3) - 1 = 87
13 + 16 + 11 + 3(16) - 1 = 87
13 + 16 + 11 + 48 - 1 = 87
87 = 87
The equation holds true, confirming that our solution x = 13 is correct.