(5x%2B6)-(x%2B1)(10x%2B17)%3D(x%2B2)-(x-7).jpeg "(2x+7)(5x+6)-(x+1)(10x+17)=(x+2)-(x-7)")
Solving the Equation: (2x+7)(5x+6)-(x+1)(10x+17)=(x+2)-(x-7)
This article will guide you through the steps involved in solving the equation: (2x+7)(5x+6)-(x+1)(10x+17)=(x+2)-(x-7).
Step 1: Expanding the products
First, we need to expand the products on both sides of the equation using the distributive property (also known as FOIL - First, Outer, Inner, Last):
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Left Side:
- (2x+7)(5x+6) = (2x * 5x) + (2x * 6) + (7 * 5x) + (7 * 6) = 10x² + 12x + 35x + 42 = 10x² + 47x + 42
- (x+1)(10x+17) = (x * 10x) + (x * 17) + (1 * 10x) + (1 * 17) = 10x² + 17x + 10x + 17 = 10x² + 27x + 17
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Right Side:
- (x+2)-(x-7) = x + 2 - x + 7 = 9
Now, the equation becomes: 10x² + 47x + 42 - (10x² + 27x + 17) = 9
Step 2: Simplifying the Equation
Next, we simplify the equation by distributing the negative sign and combining like terms:
10x² + 47x + 42 - 10x² - 27x - 17 = 9 20x + 25 = 9
Step 3: Isolating the Variable
Now, we isolate the variable 'x' by subtracting 25 from both sides:
20x + 25 - 25 = 9 - 25 20x = -16
Step 4: Solving for x
Finally, we solve for 'x' by dividing both sides by 20:
20x / 20 = -16 / 20 x = -4/5
Conclusion
Therefore, the solution to the equation (2x+7)(5x+6)-(x+1)(10x+17)=(x+2)-(x-7) is x = -4/5.