Question

linear inequalities (level 2)
question
solve the following inequality for t. write your answer in simplest form.
-7 - 4(-10t - 5) > -6t - 9 + 10t

Explanation:

Step1: Distribute the -4

First, we distribute the -4 in the term \(-4(-10t - 5)\). Using the distributive property \(a(b + c)=ab+ac\), we get \(-4\times(-10t)+(-4)\times(-5)=40t + 20\). So the left - hand side of the inequality becomes \(-7+40t + 20\). Combine like terms: \(-7 + 20=13\), so the left - hand side is \(40t+13\).

On the right - hand side, combine like terms for the \(t\) terms: \(-6t+10t = 4t\). So the right - hand side is \(4t-9\). Now our inequality is \(40t + 13>4t-9\).

Step2: Subtract 4t from both sides

Subtract \(4t\) from both sides of the inequality \(40t + 13>4t-9\) to get \(40t-4t+13>4t - 4t-9\). Simplifying both sides: \(36t+13>-9\).

Step3: Subtract 13 from both sides

Subtract 13 from both sides of the inequality \(36t + 13>-9\). We have \(36t+13 - 13>-9 - 13\). Simplifying both sides: \(36t>-22\).

Step4: Divide both sides by 36

Divide both sides of the inequality \(36t>-22\) by 36. Since 36 is positive, the direction of the inequality sign remains the same. So \(t>\frac{-22}{36}\). Simplify the fraction \(\frac{-22}{36}\) by dividing both the numerator and the denominator by 2, we get \(t>-\frac{11}{18}\).

Answer:

\(t>-\frac{11}{18}\)