How do you solve 17+3y+7y19+16y?

2 Answers
May 18, 2018

-6y

Explanation:

Collect the like terms on the left hand side
-17+10y19+16y
Take 10y from each side so that you only have y on 1 side
-1719+6y
Take 19 from each side
-366y
Finally divide each side by 6
-6y

May 18, 2018

y6

Explanation:

Solving an inequality is almost exactly like solving an equality, and for the most part you can treat it as such while solving it, except for one additional rule: whenever you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign. For example, > would go to <, to and vice versa. If you wish to know why you must do this, read the next paragraph; otherwise, you may skip it.

The reason this rule arises is because of how the number line works. Observe that if we write a<b we mean to say that a is closer to 0 than b. But, if we consider a and b, we will notice that a<b is false because a is closer to 0 than b. Therefore, when we manipulate inequalities by multiplying or dividing by a negative we must flip the inequality symbol to accurately reflect which expression is closer to zero.

Now we will solve the inequality

17+3y+7y19+16y.

So, to begin, we can solve this inequality exactly like solving an equality:

17+3y+7y19+16y=17+10y19+16y.

Adding 17 to both sides, we obtain

10y36+16y.

Now we subtract 16y from both sides:

6y36.

Now, to further simplify, we must divide by 6, and we can, but we must also remember to flip the inequality when we do so. We obtain:

y6.