I am solving inequalities then graphing my solution. in a problem such as
-2(c-1)<-22
how do i solve this? and also how do i know the greater then less then sign is going the right way?
-2(c-1)<-22
first divide both sides by negative 2 !! BUT !! remember that when you multiply (or divide) both sides of an inequality by a negative number you reverse the direction of the arrow.
so
c-1 > 11
c > 12
check
try c = 13
-2(12) < -22 ?
-24 < -22 right, good
To solve the inequality -2(c-1) < -22, you can follow these steps:
Step 1: Simplify the expression on the left side of the inequality:
Start by distributing the -2 to both terms inside the parentheses:
-2(c-1) = -2c + 2
Step 2: Rewrite the inequality with the simplified expression:
-2c + 2 < -22
Step 3: Get rid of the constant term on the right side of the inequality by subtracting 2 from both sides:
-2c < -22 - 2
-2c < -24
Step 4: Divide both sides of the inequality by -2. Since we are dividing by a negative number, the inequality sign must be flipped:
c > (-24)/(-2)
c > 12
The solution to the inequality is c > 12, which means that c is greater than 12.
Now, let's discuss how to know the correct direction of the inequality sign:
When you multiply or divide both sides of an inequality by a negative number, the inequality sign must be reversed. In this case, we divided both sides of the inequality by -2, which is a negative number, so we flipped the inequality sign from < to >.
To graph the solution, you can represent it on a number line. Mark a point at 12 and draw an arrow to the right to indicate that c is greater than 12. This will show all the possible values of c that make the inequality true.