Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+2x+1=0
-
Equation cos(x)+1=0
- Equation 25*x^2-400*x=0
- Equation -2/3x-2=6
- Express {x} in terms of y where:
- -7*x+13*y=-10
- -15*x+6*y=-1
- -15*x-7*y=-20
- -14*x-17*y=-7
-
Identical expressions
- (| two *x- seven |)= eight
- ( module of 2 multiply by x minus 7|) equally 8
- ( module of two multiply by x minus seven |) equally eight
- (|2x-7|)=8
- |2x-7|=8
-
Similar expressions
- |2*x-7|=11
- (|2*x+7|)=8
(|2*x-7|)=8 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$2 x - 7 \geq 0$$
or
$$\frac{7}{2} \leq x \wedge x < \infty$$
we get the equation
$$\left(2 x - 7\right) - 8 = 0$$
after simplifying we get
$$2 x - 15 = 0$$
the solution in this interval:
$$x_{1} = \frac{15}{2}$$
2.
$$2 x - 7 < 0$$
or
$$-\infty < x \wedge x < \frac{7}{2}$$
we get the equation
$$\left(7 - 2 x\right) - 8 = 0$$
after simplifying we get
$$- 2 x - 1 = 0$$
the solution in this interval:
$$x_{2} = - \frac{1}{2}$$
The final answer:
$$x_{1} = \frac{15}{2}$$
$$x_{2} = - \frac{1}{2}$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$2 x - 7 \geq 0$$
or
$$\frac{7}{2} \leq x \wedge x < \infty$$
we get the equation
$$\left(2 x - 7\right) - 8 = 0$$
after simplifying we get
$$2 x - 15 = 0$$
the solution in this interval:
$$x_{1} = \frac{15}{2}$$
2.
$$2 x - 7 < 0$$
or
$$-\infty < x \wedge x < \frac{7}{2}$$
we get the equation
$$\left(7 - 2 x\right) - 8 = 0$$
after simplifying we get
$$- 2 x - 1 = 0$$
the solution in this interval:
$$x_{2} = - \frac{1}{2}$$
The final answer:
$$x_{1} = \frac{15}{2}$$
$$x_{2} = - \frac{1}{2}$$
Sum and product of roots
[src]
sum
-1/2 + 15/2
$$- \frac{1}{2} + \frac{15}{2}$$
=
7
$$7$$
product
-15 ---- 2*2
$$- \frac{15}{4}$$
=
-15/4
$$- \frac{15}{4}$$
-15/4
Rapid solution
[src]
x1 = -1/2
$$x_{1} = - \frac{1}{2}$$
x2 = 15/2
$$x_{2} = \frac{15}{2}$$
x2 = 15/2