Q3. - Algebra 1

Question

Evaluate the expression $\left|f+g\right|-h$ for $f=3,g=-4$ and $h=5$ .

Step-by-Step Solution

Answer

On solving $\left|f+g\right|-h$ for $f=3,g=-4$ and $h=5$ the obtained value is $-4$ .

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

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

In $\left|f+g\right|-h$, f, g and h are variables.

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 $\left|f+g\right|-h$ where $f=3,g=-4$ and $h=5$.

Put $f=3,g=-4$ and $h=5$ in $\left|f+g\right|-h$.

$\begin{array}{c}\left|f+g\right|-h=\left|3+\left(-4\right)\right|-5\\ =\left|3-4\right|-5\\ =\left|-1\right|-5\end{array}$

Since $\left|-1\right|$ will always give a positive value. So,

$\begin{array}{c}\left|-1\right|-5=1-5\\ =-4\end{array}$

Hence, the value of $\left|f+g\right|-h$ for $f=3,g=-4$ and $h=5$ is $-4$.