Mister Exam
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- Equation:
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Equation x^2+11*x+30=0
-
Equation (-2-4t-1)²+(0+2t-1)²+(2+5t)²=9
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Equation 1/3*x=12
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Equation (|3*x-9|)-(|x+2|)=7
- Express {x} in terms of y where:
- 20*x-11*y=-8
- -12*x-20*y=7
- -9*x+7*y=14
- -8*x-4*y=-3
-
Identical expressions
- (| three *x- nine |)-(|x+ two |)= seven
- ( module of 3 multiply by x minus 9|) minus (|x plus 2|) equally 7
- ( module of three multiply by x minus nine |) minus (|x plus two |) equally seven
- (|3x-9|)-(|x+2|)=7
- |3x-9|-|x+2|=7
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Similar expressions
- (|3*x-9|)+(|x+2|)=7
- (|3*x-9|)-(|x-2|)=7
- (|3*x+9|)-(|x+2|)=7
(|3*x-9|)-(|x+2|)=7 equation
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The solution
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|3*x - 9| - |x + 2| = 7
$$- \left|{x + 2}\right| + \left|{3 x - 9}\right| = 7$$
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x + 2 \geq 0$$
$$3 x - 9 \geq 0$$
or
$$3 \leq x \wedge x < \infty$$
we get the equation
$$- (x + 2) + \left(3 x - 9\right) - 7 = 0$$
after simplifying we get
$$2 x - 18 = 0$$
the solution in this interval:
$$x_{1} = 9$$
2.
$$x + 2 \geq 0$$
$$3 x - 9 < 0$$
or
$$-2 \leq x \wedge x < 3$$
we get the equation
$$\left(9 - 3 x\right) - \left(x + 2\right) - 7 = 0$$
after simplifying we get
$$- 4 x = 0$$
the solution in this interval:
$$x_{2} = 0$$
3.
$$x + 2 < 0$$
$$3 x - 9 \geq 0$$
The inequality system has no solutions, see the next condition
4.
$$x + 2 < 0$$
$$3 x - 9 < 0$$
or
$$-\infty < x \wedge x < -2$$
we get the equation
$$\left(9 - 3 x\right) - \left(- x - 2\right) - 7 = 0$$
after simplifying we get
$$4 - 2 x = 0$$
the solution in this interval:
$$x_{3} = 2$$
but x3 not in the inequality interval
The final answer:
$$x_{1} = 9$$
$$x_{2} = 0$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x + 2 \geq 0$$
$$3 x - 9 \geq 0$$
or
$$3 \leq x \wedge x < \infty$$
we get the equation
$$- (x + 2) + \left(3 x - 9\right) - 7 = 0$$
after simplifying we get
$$2 x - 18 = 0$$
the solution in this interval:
$$x_{1} = 9$$
2.
$$x + 2 \geq 0$$
$$3 x - 9 < 0$$
or
$$-2 \leq x \wedge x < 3$$
we get the equation
$$\left(9 - 3 x\right) - \left(x + 2\right) - 7 = 0$$
after simplifying we get
$$- 4 x = 0$$
the solution in this interval:
$$x_{2} = 0$$
3.
$$x + 2 < 0$$
$$3 x - 9 \geq 0$$
The inequality system has no solutions, see the next condition
4.
$$x + 2 < 0$$
$$3 x - 9 < 0$$
or
$$-\infty < x \wedge x < -2$$
we get the equation
$$\left(9 - 3 x\right) - \left(- x - 2\right) - 7 = 0$$
after simplifying we get
$$4 - 2 x = 0$$
the solution in this interval:
$$x_{3} = 2$$
but x3 not in the inequality interval
The final answer:
$$x_{1} = 9$$
$$x_{2} = 0$$
The graph