[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
- Tell whether the value is a solution of the inequality. [tex]\sf\:14 \geq - 2 n + 4, n = - 5[/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex]14 \geq - 2 n + 4[/tex]
Swap sides so that all variable terms are on the left-hand side. This changes the sign direction.
[tex]-2n+4\leq 14 [/tex]
Subtract 4 from both sides.
[tex]-2n\leq 14-4 [/tex]
Subtract 4 from 14 to get 10.
[tex]-2n\leq 10 [/tex]
Divide both sides by -2. As -2 is <0, the inequality direction has changed.
[tex]n\geq \frac{10}{-2} \\ [/tex]
Divide 10 by -2 to get -5.
[tex] \huge \boxed{ \boxed{ \bf \: n\geq -5 }}[/tex]
- So, YES, the given value is a solution of the inequality.
