Question

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¿qué recta numérica representa el conjunto solución de la desigualdad? $-4(x + 3)leq - 2-2x$

Explanation:

Step1: Expand the left - hand side

First, expand $-4(x + 3)$ using the distributive property $a(b + c)=ab+ac$. So, $-4(x + 3)=-4x-12$. The inequality becomes $7-4x - 12\leq - 2-2x$.

Step2: Simplify the left - hand side

Combine like - terms on the left - hand side: $7-12-4x=-5 - 4x$. The inequality is now $-5-4x\leq - 2-2x$.

Step3: Add $4x$ to both sides

Adding $4x$ to both sides gives $-5\leq - 2-2x + 4x$. Simplifying the right - hand side, we get $-5\leq - 2 + 2x$.

Step4: Add 2 to both sides

Adding 2 to both sides: $-5 + 2\leq2x$, which simplifies to $-3\leq2x$.

Step5: Divide both sides by 2

Dividing both sides by 2 gives $x\geq-\frac{3}{2}=-1.5$.

Answer:

The solution set on the number line is a ray starting at $x = - 1.5$ and extending to the right (including $-1.5$), which means a closed - circle at $-1.5$ and an arrow pointing to the right.