Solve each inequality. Give the solution set using interval no...

Question

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

$7 x - 2 (x - 3) \leq 5 (2 - x)$

Accepted Answer

Hey everyone here we are asked to write the solution, set an interval notation for the following inequality of 15 X minus four times the quantity of x minus six is less than or equal to four times the quantity of four minus x. Now our first step is to apply the distributive property. So we have 15 X minus four, X plus 24 is low less than or equal to 16 minus four X. And now to find the solution of this inequality, we need to solve for X, which means we first need to get all of our X terms on the same side of our inequality. So we can first move this negative four X to the left hand side by adding four X to both sides of our inequality. And we see on the left hand side that our negative four X cancels with this positive for X. So we are just left with 15 X plus is less than or equal to 16. Now again we need to get our X variable completely alone. So we first want to move this positive 24 to the right hand side by subtracting 24 from both sides of our expression. And so we have that 15 X is less than or equal to negative eight. And now we need to get rid of our coefficient and we do this by dividing both sides by 15. And we see that X is less than or equal to negative eight divided by 15. So now we have isolated our X variable but we now need to rewrite our inequality as in interval notation. So we see that X can be less than negative 8/15. So we know that X will go from negative infinity to negative 8/15 and next we know that negative infinity gets closed by a parentheses since infinity is never included. And now looking at our inequality, we see from our symbol that we have a non strict inequality. Therefore our negative 8/15 gets closed by a bracket. So with this we have found our solution set in interval notation and so we are left with answer choice. A 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.
$7 x - 2 (x - 3) \leq 5 (2 - x)$

Key Concepts

Solving Linear Inequalities

Distributive Property

Interval Notation

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