Question

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

Explanation:

Step1: Expand the left - hand side

We have the inequality \(-(6x - 6)<40-16x\). Using the distributive property \(a(b + c)=ab+ac\) (here \(a=- 1\), \(b = 6x\), \(c=-6\)), we get \(-6x + 6<40-16x\).

Step2: Add \(16x\) to both sides

Adding \(16x\) to both sides of the inequality \(-6x + 6<40-16x\) to get all the \(x\) terms on one side.
\(-6x+16x + 6<40-16x + 16x\)
Simplifying the left - hand side: \((-6 + 16)x+6<40\), which is \(10x+6<40\).

Step3: Subtract 6 from both sides

Subtract 6 from both sides of the inequality \(10x + 6<40\):
\(10x+6 - 6<40 - 6\)
Simplifying, we get \(10x<34\).

Step4: Divide both sides by 10

Divide both sides of the inequality \(10x<34\) by 10:
\(x<\frac{34}{10}\)
Simplify \(\frac{34}{10}\) to \(\frac{17}{5}=3.4\).

Answer:

\(x < \frac{17}{5}\) (or \(x < 3.4\))