Answer
$$\frac{2}{3}x-x=-\frac{x}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{3}x-x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(\frac{2}{3}-1)x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(-\frac{1}{3})x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-\frac{x}{3}\end{aligned} $$ | |
| ① | Use the distributive property. |
| ② | Combine like terms |
| ③ | Multiply $ \dfrac{-1}{3} $ by $ x $ to get $ \dfrac{ -x }{ 3 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{-1}{3} \cdot x & \xlongequal{\text{Step 1}} \frac{-1}{3} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -1 \right) \cdot x }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -x }{ 3 } \end{aligned} $$ |
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