Question

Evaluate the expression $23-\left|3-4x\right|$ for $x=2$.

Short answer

On solving $23-\left|3-4x\right|$ for$x=2$ the obtained value is $18$ .

Step-by-step solution

Step-1. Apply the concept of Variables and Constants.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation, the constants are the values that are fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Step-2. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means the positive value of that quantity.

Example: -

Consider a variable x. Here x can be both positive or negative but $\left|x\right|$will always be positive and hence the absolute value.

Step-3. Solution of the given equation.

Given $23-\left|3-4x\right|$and $x=2$.

Put $x=2$in $23-\left|3-4x\right|$.

$\begin{array}{c}23-\left|3-4\left(2\right)\right|=23-\left|3-8\right|\\ =23-\left|-5\right|\end{array}$

Since $\left|-5\right|$will always give a positive value, so,

role="math" localid="1642186357853" $\begin{array}{c}23-\left|-5\right|=23-5\\ =18\end{array}$

Hence, the value of $23-\left|3-4x\right|$for $x=2$is $18$.