Question

Solve the inequality -3(7n+3)<6n

Answer 1

`\huge\text{Hey there!}`

`\mathsf{-3(7n + 3) < 6n}`

`\large\textsf{Distribute } \rm{-3}\large\text{ within the parentheses}`

`\mathsf{-3(7n) - 3(3) < 6n}`

`\mathsf{21n - 9 < 6n}`

`\large\textsf{Subtract }\rm{6n}\large\text{ to both sides}`

`\mathsf{-21n - 9 - 6n < 6n - 6n}`

`\large\textsf{Simplify }\large\text{it:}`

`\mathsf{-21n - 9 - 6n < 6n - 6n}`

`\large\textsf{Combine }\large\text{the like terms}`

`\mathsf{-27n - 9 < 0}`

`\large\textsf{Add }\rm{9}\large\text{ to both sides}`

`\mathsf{-27n - 9 + 9 < 0 + 9}`

`\large\textsf{Simplify}\large\text{ it}`

`\mathsf{-27n < 0 + 9}`

`\mathsf{-27n < 9}`

`\large\textsf{Divide }\rm{-27}\large\text{ to both sides}`

`\mathsf{(-27n)/(-27) < (9)/(-27)}`

`\large\textsf{Simplify }\large\text{it:}`

`\mathsf{n < (9)/(-27)}`

`\mathsf{n > (9/9)/(-27/9)}`

`\mathsf{n > -(1)/(3)}`

`\huge\text{Therefore, your answer should be: \boxed{\mathsf{n > -(1)/(3)}}}\huge\checkmark`

~
`\frak{Amphitrite\bf 1040:)}`

Answer 2

`\boxed{\sf{n > -(1)/(3)}}`

Explanation:

Isolate the term of n from one side of the equation.

Distributive property:

a(b+c)=ab+ac

-3(7n+3)<6n

-3*7n=-21n

-3*3=9

-21n-9

`\sf{-21n-9 < 6n}`

Add by 9 from both sides.

-21n-9+9<6n+9

Solve.

`\sf{-21n < 6n+9}`

Subtract by 6n from both sides.

-21<6n-6n+9-6n

Solve.

-27n<9

Multiply by -1 from both sides.

(-27n)(-1)>(9)(-1)

Solve.

27n>-9

Divide by 27 from both sides.

27n/27>-9/27

Solve.

n>-1/3

`\Rightarrow \boxed{\sf{n > -(1)/(3)}}`

The final answer is n>-1/3.

I hope this helps, let me know if you have any questions.