Solve the following inequality for tt. Write your answer in simplest form.
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
-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.
To solve the inequality, let's simplify both sides:
−7−4(−10t−5) > −6t−9+10t
Multiply -4 by -10t and -5:
−7+40t+20 > −6t−9+10t
Combine like terms on the right side:
−7+40t+20 > 4t−9
Combine like terms on the left side:
40t+13 > 4t−9
Subtract 4t from both sides:
40t-4t+13 > -9
Combine like terms on the left side:
36t+13 > -9
Subtract 13 from both sides:
36t > -22
Divide both sides by 36:
t > -22/36
Simplify -22/36:
t > -11/18
Therefore, the solution to the inequality is t > -11/18.
To solve the given inequality, let's simplify the equation step by step:
Starting with the left side:
-7 - 4(-10t - 5) > -6t - 9 + 10t
Using the distributive property, multiply -4 by (-10t) and (-4) by (-5):
-7 + 40t + 20 > -6t - 9 + 10t
Combine like terms by adding/subtracting:
40t + 13 > 4t - 9
Next, let's isolate the variable term (t). We'll do this by moving all other terms to the opposite side of the inequality:
Subtract 4t from both sides:
40t - 4t + 13 > 4t - 4t - 9
Combine like terms:
36t + 13 > -9
Subtract 13 from both sides:
36t + 13 - 13 > -9 - 13
Simplify:
36t > -22
Finally, to solve for t, divide both sides by 36:
(36t)/36 > (-22)/36
Simplify:
t > -22/36
To express the answer in simplest form, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 2:
t > -11/18
Therefore, the solution to the inequality is t > -11/18, expressed in simplest form.