# Consider these equation Evaluate 2/3 x for x= 1/2 Evaluate 1/3x+1/4 for x= 1/2 Evaluate 2/3 x...

## Question:

Consider these equation

Evaluate {eq}(2/3) x {/eq} for {eq}x= 1/2 {/eq}

Evaluate {eq}(1/3)x+1/4 {/eq} for {eq}x= 1/2 {/eq}

Evaluate {eq}(2/3) x {/eq} for {eq}x= 2 {/eq}

Evaluate {eq}(1/3)x+1/4 {/eq} for {eq}x=2 {/eq}

## Evaluating an Expression:

To evaluate an expression which is in terms of one or more variables at given values of variables, we just substitute the values of the variables in the given expression and simplify it.

We substitute the value of the variable in each of the given expressions and simplify:

(1) Substitute {eq}x= \dfrac{1}{2} {/eq} in the given expression {eq}\dfrac{2}{3}x {/eq}, then we get:

$$\dfrac{2}{3}\left(\dfrac{1}{2} \right) = \dfrac{2}{6}= \boxed{\mathbf{\dfrac{1}{3}}}$$

(2) Substitute {eq}x= \dfrac{1}{2} {/eq} in the given expression {eq}\dfrac{1}{3}x+ \dfrac{1}{4} {/eq}, then we get:

\begin{align} \dfrac{1}{3}\left( \dfrac{1}{2}\right)+ \dfrac{1}{4}&= \dfrac{1}{6}+ \dfrac{1}{2}\\[0.4cm] &= \dfrac{1}{6}+ \dfrac{3}{6} \\[0.4cm] &= \dfrac{4}{6}\\[0.4cm] &= \boxed{\mathbf{\dfrac{2}{3}}} \end{align}

(3) Substitute {eq}x=2 {/eq} in the given expression {eq}\dfrac{2}{3}x {/eq}, then we get:

$$\dfrac{2}{3}(2) = \boxed{\mathbf{\dfrac{4}{3}}}$$

(4) Substitute {eq}x=2 {/eq} in the given expression {eq}\dfrac{1}{3}x+ \dfrac{1}{4} {/eq}, then we get:

\begin{align} \dfrac{1}{3}\left( 2\right)+ \dfrac{1}{4}&= \dfrac{2}{3}+ \dfrac{1}{2}\\[0.4cm] &= \dfrac{4}{6}+ \dfrac{3}{6} \\[0.4cm] &= \boxed{\mathbf{\dfrac{7}{6}}} \end{align} 