solve, graph: Three multiplied by x subtracted by one is les

I need help to solve and graph these inequalities:

1) Three multiplied by x subtracted by one is less than eleven.

2) Two multiplied by x plus seven is greater than fifteen.

These are straightforward "translation" exercises. Where are you stuck?

Please reply showing all of your work. Thank you.

Eliz.

Re: Need help in solving this Inequality.

BR2010 said:

I need help to solve and graph this inequality.



Three multiplied by x subtracted by one is less than eleven,

or

two multiplied by x plus seven is greater than fifteen.

Click to expand...

Did you TRY translating the words of each problem into a mathematical expression?

"three multiplied by x subtracted by 1 is less than 11"

3x - 1 < 11

Ok...solve this. You solve inequalities almost identically the same way you solve equations. Let's get the variable term by itself on the left side. Add 1 to both sides of the inequality:

3x - 1 + 1 < 11 + 1

Combine like terms:

3x < 12

Divide both sides of the inequality by 3. Since we are dividing by a positive number, the direction of the inequality symbol is unchanged:

(3x) / 3 < 12 / 3

x < 4

So, this inequality should be true whenever x is a number less than 4. To graph the solution set on a number line, put an open circle at 4 on the number line (the set of numbers which "works" starts at 4, but does not include 4). Then, shade the portion of the number line to the left of 4. All numbers to the left of 4 (less than 4) satisfy the original inequality. This would be the graph of the solution.