-2/5 - 9 < 9/10
To solve the inequality -2/5 - 9 < 9/10, we can follow these steps:
Step 1: Simplify both sides of the inequality:
-2/5 - 9 < 9/10
Multiply the denominator of the first fraction (-5) by the whole number (-2):
(-2 * -5) / 5 - 9 < 9/10
10/5 - 9 < 9/10
2 - 9 < 9/10
-7 < 9/10
Step 2: Compare the left side and the right side of the inequality:
-7 < 9/10
This means that -7 is less than 9/10.
To solve this inequality, we can begin by simplifying both sides:
-2/5 - 9 < 9/10
First, let's find the common denominator for the fractions involved, which is 10:
-2/5 * 10/10 - 9 < 9/10
-20/50 - 9 < 9/10
Next, let's simplify the left side:
-20/50 - 9 = -20/50 - 450/50 = -470/50
Now, we have:
-470/50 < 9/10
To eliminate the fractions, we can multiply both sides by 50 and 10, respectively. However, since we know that 50 is a multiple of 10, we only need to multiply both sides by 50:
(-470/50) * 50 < (9/10) * 50
This simplifies to:
-470 < 45
Since -470 is less than 45, the inequality is true. Therefore, the statement -2/5 - 9 < 9/10 is true.
To solve this inequality, we need to compare the values on both sides of the inequality sign and determine if one side is less than the other side.
Let's simplify the inequality step by step:
First, let's subtract 9 from both sides:
-2/5 - 9 - 9 < 9/10 - 9
Simplifying further, we have:
-2/5 - 18 < 9/10 - 90/10
Next, let's find a common denominator for both fractions on the right side:
-2/5 - 18 < (9 - 90)/10
Simplifying the fraction on the right side, we get:
-2/5 - 18 < (-81)/10
Now, let's combine the whole numbers with the fractions on the left side:
(-2 - 18 * 5)/5 < (-81)/10
Simplifying further, we have:
(-2 - 90)/5 < (-81)/10
Combining the numbers in the numerator, we get:
(-92)/5 < (-81)/10
To make the comparison easier, we can multiply both sides by 10 to eliminate the denominators:
10 * (-92)/5 < 10 * (-81)/10
Simplifying, we have:
-184/5 < -81
Now, we just need to compare the values on both sides. In this case, -184/5 is less than -81. So, the inequality holds true.
Therefore, the original inequality -2/5 - 9 < 9/10 is true.