Solve the inequality 3t≥10−5(t+7)−1

Question

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Answer 1

To solve the inequality, we can simplify both sides and then isolate the variable t.

3t ≥ 10 - 5(t + 7) - 1

First, distribute the -5 to the expression (t + 7):

3t ≥ 10 - 5t - 35 - 1

Simplify the expression on the right side:

3t ≥ -5t - 26

Next, add 5t to both sides to get the variable term on one side:

3t + 5t ≥ -26

Combining like terms:

8t ≥ -26

Finally, divide both sides by 8 to isolate the variable t:

t ≥ -26/8

Simplifying the fraction:

t ≥ -13/4

So the solution to the inequality is t ≥ -13/4.