Mister Exam

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|x+4|+|x-5|=8 equation

The teacher will be very surprised to see your correct solution 😉

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|x + 4| + |x - 5| = 8

\left|{x - 5}\right| + \left|{x + 4}\right| = 8

Simplify

Detail solution

For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.

1.

x - 5 \geq 0

x + 4 \geq 0

5 \leq x \wedge x < \infty

we get the equation

\left(x - 5\right) + \left(x + 4\right) - 8 = 0

after simplifying we get

2 x - 9 = 0

the solution in this interval:

x_{1} = \frac{9}{2}

but x1 not in the inequality interval

2.

x - 5 \geq 0

x + 4 < 0

The inequality system has no solutions, see the next condition

3.

x - 5 < 0

x + 4 \geq 0

-4 \leq x \wedge x < 5

we get the equation

\left(5 - x\right) + \left(x + 4\right) - 8 = 0

after simplifying we get
incorrect
the solution in this interval:

4.

x - 5 < 0

x + 4 < 0

-\infty < x \wedge x < -4

we get the equation

\left(5 - x\right) + \left(- x - 4\right) - 8 = 0

after simplifying we get

- 2 x - 7 = 0

the solution in this interval:

x_{2} = - \frac{7}{2}

but x2 not in the inequality interval

The final answer:

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Sum and product of roots [src]

sum

0

0

product

1

1