Question

question
solve the following inequality for t. write your answer in simplest form.
9 + 3(-3t + 10) ≤ 6t + 8 - 4
answer attempt 1 out of 2
t <
submit answer

Explanation:

Step1: Expand the left - hand side

$9+3(-3t + 10)=9-9t+30=39 - 9t$.
The right - hand side is $6t + 8-4=6t + 4$.
So the inequality becomes $39-9t\leqslant6t + 4$.

Step2: Move terms with $t$ to one side

Add $9t$ to both sides: $39\leqslant6t + 9t+4$, that is $39\leqslant15t + 4$.

Step3: Move the constant term to the other side

Subtract 4 from both sides: $39 - 4\leqslant15t$, so $35\leqslant15t$.

Step4: Solve for $t$

Divide both sides by 15: $t\geqslant\frac{35}{15}=\frac{7}{3}$.

Answer:

$t\geqslant\frac{7}{3}$