[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
[tex] \sf1 - 3 n \gt - 1 - 4 ( 2 n - 8 )[/tex]
- Solve the inequality algebraically.
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \sf1 - 3 n \gt - 1 - 4 ( 2 n - 8 )[/tex]
- Use the distributive property to multiply -4 by 2n-8.
[tex] \sf1-3n>-1-8n+32 [/tex]
[tex] \sf1-3n>31-8n [/tex]
[tex] \sf1-3n+8n>31 [/tex]
- Combine -3n and 8n to get 5n.
[tex] \sf1+5n>31 [/tex]
- Subtract 1 from both sides.
[tex] \sf5n>31-1 [/tex]
- Subtract 1 from 31 to get 30.
[tex] \sf5n>30 [/tex]
- Divide both sides by 5. As 5 > 0, the direction of the inequality remains the same.
[tex] \sf \: n>\frac{30}{5} \\ [/tex]
[tex] \boxed{ \boxed{ \bf \: n>6 }}[/tex]
