Solve: negative 1 over 2x + 2 = -x + 7

Solution:

Given negative 1 over 2x + 2 = -x + 7

We denote the given expression as -1/(2x + 2) = -x + 7

To find the solution, we must keep all ‘x’ terms on one side of the equation(i.e. isolate the variable x)

Multiply by “2x + 2” on both sides, we get

-1 = (-x + 7)(2x + 2)

-1 = -2x² - 2x + 14x + 14

Add ‘1’ on both sides, we get

-2x² - 2x + 14x + 14 + 1 = 0

-2x² + 12x + 15 = 0

This is a quadratic equation, so we need to find factors using quadratic formula

x= -b ± √(b² - 4ac)/2a

Here, a = -2, b = 12, c = 15

x = -12 ± √(12² - 4(-2)(15) / 2(-2)

x = -12 ± √(12² +120) / -4

x = -12 ± √(144 + 120) / -4

x= -12 ± (√264) / -4

x= -12 ± 16.2 /-4

x= -1.05, 7.05

The solutions for the given expression are -1.05 and 7.05

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Solve: negative 1 over 2x + 2 = -x + 7

Summary:

By solving negative 1 over 2x + 2 = -x + 7, we get solutions as -1.05 and 7.05