Questions: 4 ≤ -4x - 8 < 12

4 ≤ -4x - 8 < 12
Transcript text: $4 \leq-4 x-8<12$
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Solution

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Solution Steps

To solve the compound inequality \(4 \leq -4x - 8 < 12\), we need to break it into two separate inequalities and solve each one individually. Then, we combine the solutions to find the range of \(x\) that satisfies both inequalities.

Step 1: Despejar la desigualdad

Primero, vamos a resolver la desigualdad \(4 \leq -4x - 8 < 12\) paso a paso.

Step 2: Añadir 8 a todos los lados

Añadimos 8 a todos los lados de la desigualdad para simplificar:

\[ 4 + 8 \leq -4x - 8 + 8 < 12 + 8 \]

Esto nos da:

\[ 12 \leq -4x < 20 \]

Step 3: Dividir por -4 y cambiar el sentido de las desigualdades

Dividimos todos los lados por -4. Recordemos que al dividir por un número negativo, el sentido de las desigualdades cambia:

\[ \frac{12}{-4} \geq x > \frac{20}{-4} \]

Esto se simplifica a:

\[ -3 \geq x > -5 \]

Step 4: Reescribir la desigualdad en forma estándar

Reescribimos la desigualdad en una forma más estándar:

\[ -5 < x \leq -3 \]

Final Answer

\[ \boxed{-5 < x \leq -3} \]

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