- #1
Alexstrasuz1
- 20
- 0
I have trouble solving this equation
|1/2x+1|=|x|
My answers are x=2 and x=-2/3
|1/2x+1|=|x|
My answers are x=2 and x=-2/3
Last edited:
Alexstrasuz said:I have trouble solving this equation
|1/2x+1|=|x|
My answers are x=2 and x=-2/3
chisigma said:An easy way is to find the solution of the equations...
$\displaystyle \frac{1}{2 x} + 1 = x \implies 2\ x^{2} - 2\ x - 1 =0 \implies x = \frac{1 \pm \sqrt{3}}{2}\ (1)$
$\displaystyle \frac{1}{2 x} + 1 = - x \implies 2\ x^{2} + 2\ x - 1 =0 \implies x = \frac{- 1 \pm \sqrt{3}}{2}\ (2)$
Kind regards
$\chi$ $\sigma$
Alexstrasuz said:I have trouble solving this equation
|1/2x+1|=|x|
My answers are x=2 and x=-2/3
RLBrown said:Yes, your answers are correct.
Other posts were solving...
|1/2/x+1|=|x|
An absolute value equation is an equation that contains the absolute value of a variable. The absolute value of a number is its distance from zero on a number line. So, an absolute value equation is an equation that includes an expression within absolute value bars.
To solve an absolute value equation algebraically, you need to isolate the absolute value expression on one side of the equation. Then, you need to create two separate equations, one with the positive value of the expression and one with the negative value. Solve both equations to find the two possible solutions.
Yes, an absolute value equation can have more than two solutions. This is because the absolute value of a number can be the same for multiple values, such as |-5| = |5| = 5. So, an equation with absolute value can have as many solutions as there are values that make the absolute value expression equal to the given value.
An absolute value equation is an equation, while an absolute value inequality is an inequality. The main difference is that an equation has an equals sign, while an inequality has a greater than or less than sign. Also, an absolute value equation will have a specific solution, while an absolute value inequality will have a range of possible solutions.
Absolute value equations are important in real-world applications because they are used to solve many real-life problems. For example, they can be used to find the distance between two points on a map or the amount of money needed to reach a certain goal. They are also used in physics, engineering, and other fields to model and solve various problems.