k/5+3/20<3/10
Please help me solve this and show your work please and thank you
To solve the inequality k/5 + 3/20 < 3/10, we can follow these steps:
Step 1: Find a common denominator for all the fractions involved. In this case, the least common denominator (LCD) is 20 (which is a multiple of both 5 and 20).
Step 2: Multiply each fraction by the necessary factor to obtain a denominator of 20.
For the first fraction, k/5, multiply the numerator and denominator by 4: (k * 4)/(5 * 4) = 4k/20.
For the second fraction, 3/20, it already has a denominator of 20.
For the third fraction, 3/10, multiply the numerator and denominator by 2: (3 * 2)/(10 * 2) = 6/20.
After carrying out the necessary operations, the inequality becomes:
4k/20 + 3/20 < 6/20.
Step 3: Combine the fractions on the left side of the inequality by adding their numerators together:
(4k + 3)/20 < 6/20.
Step 4: Now, we can solve for k. To isolate k, we can multiply both sides of the inequality by 20 (the denominator):
20 * (4k + 3)/20 < 20 * 6/20.
Simplifying further, we get:
4k + 3 < 6.
Step 5: Solve for k by isolating it on one side of the inequality.
Subtract 3 from both sides of the equation:
4k < 6 - 3,
4k < 3.
Step 6: Divide both sides of the equation by 4 to solve for k:
(4k)/4 < 3/4,
k < 3/4.
The solution to the inequality is k < 3/4.