Question

question 14
solve the inequality.
-5(6y - 7) < -35y - 10
○ x < -9
○ x > -9
○ x > -10
○ x < -10

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b - c)=ab - ac\), we have \(-5(6y - 7)=-5\times6y-(-5)\times7=-30y + 35\). So the inequality becomes \(-30y + 35<-35y - 10\).

Step2: Add \(35y\) to both sides

Adding \(35y\) to both sides of the inequality \(-30y + 35<-35y - 10\) gives \(-30y+35y + 35<-35y+35y - 10\), which simplifies to \(5y + 35<-10\).

Step3: Subtract 35 from both sides

Subtracting 35 from both sides of \(5y + 35<-10\) gives \(5y+35 - 35<-10 - 35\), so \(5y<-45\).

Step4: Divide both sides by 5

Dividing both sides of \(5y<-45\) by 5 (since 5 is positive, the inequality sign remains the same) gives \(y<-9\). Wait, there is a typo in the options (using \(x\) instead of \(y\)), but following the options' variable, the solution is \(x < - 9\) (assuming a typo in variable name).

Answer:

A. \(x < -9\)