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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.

Answer and Explanation:

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:

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


Learn more about this topic:

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Evaluating Simple Algebraic Expressions

from ELM: CSU Math Study Guide

Chapter 6 / Lesson 3
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