Solve each inequality. Give the solution set using interval notat...

Question

Solve each inequality. Give the solution set using interval notation. 11x≥2(x-4)

Accepted Answer

Hey everyone here we are asked to write the solution set in interval notation for the following inequality of seven, X is greater than or equal to three times the quantity of x minus six. So to write the solution set of this given inequality we need to solve for X. And so we first want to just apply the distributive property for this three on the right hand side. So our expression becomes seven X is greater than or equal to three x minus 18. And now we just want to get all of our X terms on the same side of this expression here. So we want to subtract three X from both sides. So we move three X from the right hand side to the left hand side. So now we have seven X minus three X is greater than or equal to negative 18. And now just simplifying our like terms here, seven x minus three X gives us four X is greater than or equal to negative 18. And now we need to get rid of this coefficient for X. So we just need to divide both sides by four. And we see in our expression we have X is greater than or equal to negative 18, divided by four, simplifying. We see that X is greater than or equal to negative nine halves. And so now we need to write this simplified inequality as a solution set and we see that our inequality here we have greater than or equal to so we have a non strict inequality which tells us that our negative nine halves gets closed by a bracket. And so we have that X is within negative nine halves, again being closed by a bracket. And we see that X is also greater than this value, or can be greater than so we go to positive infinity, which is not included, so it gets closed by a parentheses. And with this we have found our solution set and therefore we are left with the answer choice. C. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

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Solve each inequality. Give the solution set using interval notation. 11x≥2(x-4)

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