Question

what values of x solve the following inequality? -6(6x - 6) < 40 - 16x

Explanation:

Step1: Expand the left - hand side

We have the inequality \(-6(6x - 6)<40 - 16x\).
Using the distributive property \(a(b - c)=ab - ac\), where \(a=-6\), \(b = 6x\) and \(c = 6\), we get:
\(-6\times6x-(-6)\times6<40 - 16x\)
\(-36x + 36<40 - 16x\)

Step2: Move the \(x\) terms to one side

Add \(36x\) to both sides of the inequality to get all the \(x\) terms on one side.
\(-36x+36 + 36x<40 - 16x+36x\)
Simplifying both sides, we have:
\(36<40 + 20x\)

Step3: Isolate the constant term on the left - hand side

Subtract 40 from both sides of the inequality:
\(36-40<40 + 20x-40\)
Simplifying both sides gives:
\(-4<20x\)

Step4: Solve for \(x\)

Divide both sides of the inequality by 20:
\(\frac{-4}{20}<\frac{20x}{20}\)
Simplifying the fractions, we get:
\(-\frac{1}{5}-\frac{1}{5}\)

Answer:

\(x>-\frac{1}{5}\)