Solve the following inequality for n. Write your answer in simplest form.
1+4(-6n-4)<10n+4-n

Answer

n>- 19/33

1 Simplify  10n+4-n10n+4−n  to  9n+49n+4.

1+4(-6n-4)<9n+41+4(−6n−4)<9n+4

2 Expand.

1-24n-16<9n+41−24n−16<9n+4

3 Simplify  1-24n-161−24n−16  to  -24n-15−24n−15.

-24n-15<9n+4−24n−15<9n+4

4 Add 24n24n to both sides.

-15<9n+4+24n−15<9n+4+24n

5 Simplify  9n+4+24n9n+4+24n  to  33n+433n+4.

-15<33n+4−15<33n+4

6 Subtract 44 from both sides.

-15-4<33n−15−4<33n

7 Simplify  -15-4−15−4  to  -19−19.

-19<33n−19<33n

8 Divide both sides by 3333.

-\frac{19}{33}<n−

33

19

<n

9 Switch sides.

n>-\frac{19}{33}n>−

33

19

Done