# Could you explain how to solve the given type of problem. (c)Absolute value equation: |2x-5|=7

Question
Piecewise-Defined Functions
Could you explain how to solve the given type of problem.
(c)Absolute value equation: $$|2x-5|=7$$

2021-03-03
The given absolute value equation is $$|2x-5|=7$$.
The absolute value of a number x is given by:
$$|x|=\left\{(x,\ if\ x\geq 0),(-x, if x<0)\right\}$$</span>
This represents the distance of x from the origin on the real number line.
To solve absolute value equation, solve two separate equations as,
$$2x-5=7$$ or $$2x-5=-7$$
Thus, the absolute value equation can be solved by property of absolute value number.

### Relevant Questions

Solve the absolute value equation.
$$\displaystyle-{7}{\left({y}+{5}\right)}{<}-{9}{y}-{35}$$
How do you solve an equation inequality an absolute value?
How do you solve an equation involving an absolute value?
Solve the absolute value equation or indicate the equation has no solution: $$\displaystyle{\left|{2}{x}-{3}\right|}={11}$$
Find the absolute maximum and absolute minimum values of f on the given interval.
$$\displaystyle{f{{\left({x}\right)}}}={5}+{54}{x}-{2}{x}^{{{3}}},{\left[{0},{4}\right]}$$
Find the absolute maximum and absolute minimum values of function on the given interval.
$$\displaystyle{f{{\left({x}\right)}}}={5}+{54}{x}-{2}{x}^{{3}},{\left[{0},{4}\right]}$$
Find the absolute maximum and absolute minimum values of f on the given interval.
$$\displaystyle{f{{\left({x}\right)}}}={5}+{54}{x}-{2}{x}^{{3}},{x}\in{\left[{0},{4}\right]}$$
Find the absolute value of the following numbers.
a. $$\displaystyle{\left|{{7}}\right|}=$$?
b. $$\displaystyle{\left|{-{7}}\right|}=$$?
c. $$\displaystyle-{\left|{{7}}\right|}=$$?
d. $$\displaystyle-{\left|{-{7}}\right|}=$$?
a)$$\displaystyle{\left|{-{7}}\right|}$$
b)$$\displaystyle{\left|{-{2}}\right|}$$
c)$$\displaystyle{\left|{{6}}\right|}$$
d)$$\displaystyle{\left|{{0}}\right|}$$