Solve the following inequality for tt. Write your answer in simplest form.

Question

minus, 7, minus, 4, left bracket, minus, 10, t, minus, 5, right bracket, is greater than, minus, 6, t, minus, 9, plus, 10, t
−7−4(−10t−5)>
−6t−9+10t

Answer 1

-7 - 4(-10t - 5) > -6t - 9 + 10t

Start by distributing the -4 to the terms inside the parentheses:

-7 + 40t + 20 > -6t - 9 + 10t

Combine like terms on each side of the inequality:

40t + 20 - 7 > 4t - 9

40t + 13 > 4t - 9

Next, move all terms containing t to one side of the inequality by subtracting 4t from both sides:

40t - 4t + 13 > -9

36t + 13 > -9

Finally, isolate t by subtracting 13 from both sides:

36t > -9 - 13

36t > -22

t > -22/36

Simplified, t > -11/18.