How do I solve inequalities? For example a+15>27. a.) a>42 b.) a>13 c.) a>12 d.) not given.
You can add or subtract numbers or variables from both sides of inequalities and they remain valid. You can also multiply or divide either side by positive numbers. The direction of the inequality sign witll not change. If you multiply or divide both sides by negative numbers, the direction of the inequality sign must then change.
Example:
a + 15 > 27
Subtract 15 from both sides:
a > 12 is the answer. That is answer (c)
OK I understand that, but what do you do if it's something like
8y - 21 < 7y + 3?
add 21 to both sides
8 y < 7 y + 24
subtract 7 y from both sides
y < 24
Ok I can do that, but this question is different.
7y + 13 < 9y - 8
Ok I added 8 to both sides and got
7y + 21 < 9y
Then I subtracted 7y from both sides
21 < 2y
Now I'm stuck
divide both sides by 2
divide both sides by 2
10.5 <y
so y >10.5
is the more common way to write that
To solve inequalities, follow these steps:
Step 1: Isolate the variable on one side of the inequality.
In your example, the variable "a" is already isolated on one side.
Step 2: Simplify both sides of the inequality if needed.
a + 15 > 27 - Subtracting 15 from both sides gives:
a > 12
Step 3: Identify the correct inequality symbol.
The inequality symbol ">" indicates "greater than." Therefore, the answer is:
c.) a > 12
To verify this answer, you can substitute a value greater than 12 into the inequality and check if it holds true. Similarly, you can substitute a value less than 12 and see if the inequality is false.