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

Question

Solve each inequality. Give the solution set using interval notation. -5x - 4≥3(2x-5)

Accepted Answer

Hey everyone here we are asked to write the solution set in interval notation for the following inequality of negative eight, X minus 23 is greater than or equal to two times the quantity of five x minus four. Now to find the solution set, we first need to find the solution of our inequality by solving for X. So first we need to use the distributive property on the right hand side of our inequality. And so our expression becomes negative eight, X minus 23 is greater than or equal to x minus eight. Now we need to solve for X. So we first need to get all of our X terms on the same side of the inequality. So we can go ahead and move this positive 10 X to the left hand side by subtracting 10 X from both sides of our inequality and this gives us the expression neck 18 X minus 23 is greater than or equal to negative eight. Now again we need to get X completely isolated. So next we just want to move this negative 23 to the right hand side by adding 23 to both sides of the inequality. And so we have negative 18, X is greater than or equal to 15. And now we need to get rid of our coefficient and we do this by by dividing both sides by negative 18. But since we are dividing by negative 18, a negative value in our inequality we need to flip the sign. So we get that X is now less than or equal to negative 15 divided by 18. And now simplifying, we see that X is less than or equal to five, negative 56. So now we just need to rewrite our inequality that we have in interval notation. So first we see that X can be less than negative 56. So we know that X will go from negative infinity to negative 56. And now we know that that infinity signs are always excluded. So our negative infinity gets closed by a parenthesis. And now looking at our inequality symbol, we see that we have a non strict inequality. Therefore our negative 56 gets closed by a bracket. So with this we have found our interval notation for our solution set and so we are left with answer choice B. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Solve each inequality. Give the solution set using interval notation. -5x - 4≥3(2x-5)

Key Concepts

Inequalities

Interval Notation

Algebraic Manipulation

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