Question

determinar si cada valor de x es una solución de 51≥9x−3.
x | ¿es una solución? | |

sí

no

−1 | ○ | ○ |
7 | ○ | ○ |
−3 | ○ | ○ |
6 | ○ | ○ |

Explanation:

Step1: Solve the inequality for x

First, we solve the inequality \(51 \geq 9x - 3\). Add 3 to both sides:
\(51 + 3 \geq 9x - 3 + 3\)
\(54 \geq 9x\)

Then divide both sides by 9:
\(\frac{54}{9} \geq \frac{9x}{9}\)
\(6 \geq x\) or \(x \leq 6\)

Step2: Check each value of x

• For \(x = -1\):

Since \(-1 \leq 6\), substitute into the original inequality: \(9(-1) - 3 = -9 - 3 = -12\). Check if \(51 \geq -12\): Yes. So \(x = -1\) is a solution (Sí).

• For \(x = 7\):

Since \(7 > 6\), substitute: \(9(7) - 3 = 63 - 3 = 60\). Check if \(51 \geq 60\): No. So \(x = 7\) is not a solution (No).

• For \(x = -3\):

Since \(-3 \leq 6\), substitute: \(9(-3) - 3 = -27 - 3 = -30\). Check if \(51 \geq -30\): Yes. So \(x = -3\) is a solution (Sí).

• For \(x = 6\):

Since \(6 \leq 6\), substitute: \(9(6) - 3 = 54 - 3 = 51\). Check if \(51 \geq 51\): Yes (equality holds). So \(x = 6\) is a solution (Sí).

Answer:

\(x\)	¿Es una solución?
\(-1\)	⚫
\(7\)		⚫
\(-3\)	⚫
\(6\)	⚫

(Note: "⚫" indicates the correct option is selected. For \(x=-1\), \(-3\), \(6\) select "Sí"; for \(x=7\) select "No".)