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10. Skriv ett uttryck i den tomma parentesen så att likheten gäller. \( 3(4 x-10)=2( \)

Ask by Matthews Colon. in Sweden
Dec 12,2024

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Skriv \( 6x - 15 \) i den tomma parentesen så att likheten gäller.

Solución

För att lösa uttrycket \( 3(4x - 10) = 2( \) så behöver vi först förenkla vänster sida av ekvationen. Vi börjar med att distribuera \( 3 \) på vänster sida: \[ 3(4x - 10) = 12x - 30 \] Nu har vi: \[ 12x - 30 = 2( \) \] För att få ett uttryck i den tomma parentesen som gör att likheten gäller, kan vi dela hela vänster sida med \( 2 \): \[ \frac{12x - 30}{2} = 6x - 15 \] Så vi kan skriva: \[ 3(4x - 10) = 2(6x - 15) \] Därmed är uttrycket som ska stå i den tomma parentesen \( 6x - 15 \). Alltså, svaret är: \[ 6x - 15 \]

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The Deep Dive

För att lösa uttrycket kan vi börja med att förenkla vänstra sidan: \( 3(4x - 10) = 12x - 30 \). Vi behöver å sin sida få reda på vad som ska stå i den tomma parentesen för att värdet av uttrycket ska bli lika. Vi kan uttrycka det som: \( 12x - 30 = 2(\text{vad som helst}) \). Om vi nu delar båda sidor med 2 får vi \( 6x - 15 \). Så det korrekta uttrycket som ska in i den tomma parentesen är \( 6x - 15 \). Så, den fullständiga likheten blir: \( 3(4x - 10) = 2(6x - 15) \).

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