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Risolvi le equazioni applicando la regola del trasporto, come nell'esempio. \( \begin{array}{l}2-x=5-2 x \\ 1+13 x=9+12 x \\ \\ 9 x+6=4+8 x \\ \text { d. } 5 x-11=4 x-15 \\ \text { Risolvi le equazioni applicando la regola di cancellazione, come nell'esempio. } \\ \text { 10x } x+x=10 x-1 \\ \text { a } 16 x-1 \rightarrow x=-1 \\ \text { b. } 16 x=16 x-2 \\ \text { c } x+9+2 x=4+2 x+9 \\ \text { d } 24+x=24-6\end{array} \)

Ask by Bowers Cox. in Italy
Mar 13,2025

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Ecco le soluzioni delle equazioni: 1. \( 2 - x = 5 - 2x \) → \( x = 3 \) 2. \( 1 + 13x = 9 + 12x \) → \( x = 8 \) 3. \( 9x + 6 = 4 + 8x \) → \( x = -2 \) 4. \( 5x - 11 = 4x - 15 \) → \( x = -4 \) 5. \( 10x + x = 10x - 1 \) → \( x = -1 \) 6. \( 16x = 16x - 2 \) → Nessuna soluzione 7. \( x + 9 + 2x = 4 + 2x + 9 \) → \( x = 4 \) 8. \( 24 + x = 24 - 6 \) → \( x = -6 \)

Solución

Solve the equation by following steps: - step0: Solve for \(x\): \(24+x=24-6\) - step1: Cancel equal terms: \(x=-6\) Solve the equation \( 5x-11=4x-15 \). Solve the equation by following steps: - step0: Solve for \(x\): \(5x-11=4x-15\) - step1: Move the expression to the left side: \(5x-4x=-15+11\) - step2: Add and subtract: \(x=-15+11\) - step3: Add and subtract: \(x=-4\) Solve the equation \( 16x=16x-2 \). Solve the equation by following steps: - step0: Solve for \(x\): \(16x=16x-2\) - step1: Cancel equal terms: \(0=-2\) - step2: The statement is false: \(x \in \varnothing \) Solve the equation \( x+9+2x=4+2x+9 \). Solve the equation by following steps: - step0: Solve for \(x\): \(x+9+2x=4+2x+9\) - step1: Cancel equal terms: \(x+2x=4+2x\) - step2: Cancel equal terms: \(x=4\) Solve the equation \( 1+13x=9+12x \). Solve the equation by following steps: - step0: Solve for \(x\): \(1+13x=9+12x\) - step1: Move the expression to the left side: \(13x-12x=9-1\) - step2: Add and subtract: \(x=9-1\) - step3: Add and subtract: \(x=8\) Solve the equation \( 2-x=5-2x \). Solve the equation by following steps: - step0: Solve for \(x\): \(2-x=5-2x\) - step1: Move the expression to the left side: \(-x+2x=5-2\) - step2: Add and subtract: \(x=5-2\) - step3: Add and subtract: \(x=3\) Solve the equation \( 9x+6=4+8x \). Solve the equation by following steps: - step0: Solve for \(x\): \(9x+6=4+8x\) - step1: Move the expression to the left side: \(9x-8x=4-6\) - step2: Add and subtract: \(x=4-6\) - step3: Add and subtract: \(x=-2\) Solve the equation \( 10x+x=10x-1 \). Solve the equation by following steps: - step0: Solve for \(x\): \(10x+x=10x-1\) - step1: Cancel equal terms: \(x=-1\) Ecco le soluzioni delle equazioni applicando la regola del trasporto e la regola di cancellazione: ### Equazioni con la regola del trasporto: 1. **Equazione:** \( 2 - x = 5 - 2x \) - **Soluzione:** \( x = 3 \) 2. **Equazione:** \( 1 + 13x = 9 + 12x \) - **Soluzione:** \( x = 8 \) 3. **Equazione:** \( 9x + 6 = 4 + 8x \) - **Soluzione:** \( x = -2 \) 4. **Equazione:** \( 5x - 11 = 4x - 15 \) - **Soluzione:** \( x = -4 \) ### Equazioni con la regola di cancellazione: 1. **Equazione:** \( 10x + x = 10x - 1 \) - **Soluzione:** \( x = -1 \) 2. **Equazione:** \( 16x = 16x - 2 \) - **Soluzione:** \( x \in \varnothing \) (non ha soluzioni) 3. **Equazione:** \( x + 9 + 2x = 4 + 2x + 9 \) - **Soluzione:** \( x = 4 \) 4. **Equazione:** \( 24 + x = 24 - 6 \) - **Soluzione:** \( x = -6 \) Se hai bisogno di ulteriori chiarimenti o di altre equazioni, fammi sapere!

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Per risolvere le equazioni applicando la regola del trasporto, iniziamo con la prima equazione. Abbiamo \(2 - x = 5 - 2x\): sommiamo \(2x\) a entrambi i lati, ottenendo \(2 + x = 5\), da cui \(x = 3\). Passando alla seconda equazione \(1 + 13x = 9 + 12x\): sottraiamo \(12x\) e \(1\) a entrambi i lati, da cui \(x = 8\). Analizziamo ora \(9x + 6 = 4 + 8x\): sottraendo \(8x\) e \(6\), troviamo \(x = -2\), mentre per \(5x - 11 = 4x - 15\): aggiungendo \(11\) e \(4x\), abbiamo \(x = -4\). Passando alle equazioni applicando la regola di cancellazione: per \(10x + x = 10x - 1\), semplificando il termine \(10x\) da entrambi i lati, otteniamo \(x = -1\). In \(16x = 16x - 2\) non possiamo risolvere ulteriormente poiché è una tautologia. Per \(x + 9 + 2x = 4 + 2x + 9\), cancelliamo \(2x\) e \(9\) per trovare \(x = 4\). Infine, per \(24 + x = 24 - 6\), sottraendo \(24\) da entrambi i lati, otteniamo \(x = -6\).

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