Example Question - variable g
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Solving Inequalities with Variable g
The inequality given in the image is: 5g + 3 ≤ 37 To solve for g, we follow these steps: 1. Subtract 3 from both sides to isolate the term with g on one side: 5g + 3 - 3 ≤ 37 - 3 Which simplifies to: 5g ≤ 34 2. Now, divide both sides by 5 to solve for g: \( \frac{5g}{5} \) ≤ \( \frac{34}{5} \) This gives us: g ≤ 6.8 So, any value of g that is less than or equal to 6.8 will satisfy the inequality. Looking at the options provided: - g = 8: this does not satisfy the inequality because 8 is greater than 6.8. - g = 5: this does satisfy the inequality because 5 is less than 6.8. - g = -2: this also satisfies the inequality because -2 is less than 6.8. - g = -1: this too satisfies the inequality because -1 is less than 6.8. Since three of the options satisfy the inequality and we are asked for a solution to the inequality, we have to identify which one of the options is correct. Based on the information provided in the image, it seems we are asked for a single solution, but there are three possible solutions. In this scenario, without further information, it would be best to state that g = 5, g = -2, and g = -1 all are solutions to the given inequality since they all result in a true statement when substituted back into the inequality.
Simplifying a Mathematical Expression with Variable G
El problema de la imagen está parcialmente cortado y no proporciona toda la información necesaria como para responder completamente a la pregunta. Sin embargo, parece que la parte visible de la pregunta está pidiendo simplificar una expresión matemática que involucra la variable G. La expresión que se muestra es: \[ G = \frac{1}{3} + \frac{G}{3} \] Para resolverla, necesitas despejar G. Aquí está el proceso en español: Primero, vamos a obtener un denominador común para combinar los términos fraccionarios: \[ G = \frac{1}{3} + \frac{G}{3} \] Como ambos términos tienen el mismo denominador, puedes sumar los numeradores: \[ G = \frac{1 + G}{3} \] Ahora, multiplica ambos lados de la ecuación por 3 para deshacerse del denominador: \[ 3 \cdot G = 1 + G \] Distribuye 3 en el lado izquierdo: \[ 3G = 1 + G \] Para despejar G, vamos a restar G de ambos lados de la ecuación: \[ 3G - G = 1 \] Esto nos da: \[ 2G = 1 \] Por último, divide ambos lados entre 2 para obtener G solo: \[ G = \frac{1}{2} \] Por lo tanto, el valor de G es \(\frac{1}{2}\) o 0.5. Ten en cuenta que solo pude ver y trabajar con la parte visible de la imagen. Si hay más información o instrucciones adicionales en el resto del problema que no puedo ver, necesitaría esa información para proporcionar una asistencia más completa.
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