To solve the inequality [tex]\(\frac{x}{3} \geq -6\)[/tex], follow these steps:
1. Isolate the variable [tex]\(x\)[/tex]:
To eliminate the fraction, multiply both sides of the inequality by 3, the denominator of the fraction:
[tex]$
\frac{x}{3} \times 3 \geq -6 \times 3
$[/tex]
2. Simplify each side:
[tex]$
x \geq -18
$[/tex]
3. Interpret the solution:
The inequality [tex]\(x \geq -18\)[/tex] means that [tex]\(x\)[/tex] must be greater than or equal to [tex]\(-18\)[/tex]. In interval notation, this can be represented as:
[tex]$
[-18, \infty)
$[/tex]
4. Write the final solution:
In terms of inequalities, the solution is:
[tex]$
x \geq -18
$[/tex]
Thus, the solution to the inequality [tex]\(\frac{x}{3} \geq -6\)[/tex] is [tex]\(x \geq -18\)[/tex].
