Question
Answer
$$(2-x)\cdot3-3\cdot(2-x)\cdot2+2\cdot(2-x)+5=x+3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2-x)\cdot3-3\cdot(2-x)\cdot2+2\cdot(2-x)+5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6-3x-(6-3x)\cdot2+4-2x+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6-3x-(12-6x)+4-2x+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6-3x-12+6x+4-2x+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3x-6+4-2x+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}x-2+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x+3\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{2-x}\right) \cdot 3 = 6-3x $$Multiply $ \color{blue}{3} $ by $ \left( 2-x\right) $ $$ \color{blue}{3} \cdot \left( 2-x\right) = 6-3x $$Multiply $ \color{blue}{2} $ by $ \left( 2-x\right) $ $$ \color{blue}{2} \cdot \left( 2-x\right) = 4-2x $$ |
| ② | $$ \left( \color{blue}{6-3x}\right) \cdot 2 = 12-6x $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 12-6x \right) = -12+6x $$ |
| ④ | Combine like terms: $$ \color{blue}{6} \color{red}{-3x} \color{blue}{-12} + \color{red}{6x} = \color{red}{3x} \color{blue}{-6} $$ |
| ⑤ | Combine like terms: $$ \color{blue}{3x} \color{red}{-6} + \color{red}{4} \color{blue}{-2x} = \color{blue}{x} \color{red}{-2} $$ |
| ⑥ | Combine like terms: $$ x \color{blue}{-2} + \color{blue}{5} = x+ \color{blue}{3} $$ |
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