How do you solve #\frac { m } { 3} - 3

Question

How do you solve #\frac { m } { 3} - 3< \frac { 4} { 3} - \frac { m } { 2}#?

Eva Abramson · Accepted Answer

#m < 26/5#

#m < 5 1/5#

#m <5.2# The fractions can be eliminated right away. Multiply all of the inequality's terms by the #LCD#, or #6#. By doing this, you will be able to eliminate the fractions completely by canceling the denominators. #(blue)(6xx)m)/3-color(blue)(6xx3) < (blue)(6xx)4)/3 - (blue)(6xxm))/2# #(blue)(cancel6^2xx)m)/cancel3-blue)(6xx3) < (blue)(cancel6^2xx)4)/cancel3 - (blue)(cancel6^3xxm))/cancel2# Rearrange the terms "#rarr 2m-18 < 8-3m" #2m+3m <8+18# #5m < 26# #m < 26/5# This corresponds to #m < 5 1/5 " or " m <5.2#."

Nathan Axel · Answer

undefined To solve the inequality $ \frac{m}{3} - 3 < \frac{4}{3} - \frac{m}{2} $, we can follow these steps:

1. First, let's get rid of the fractions by multiplying both sides of the inequality by the least common denominator (LCD), which is 6.
2. After multiplying, simplify the expression.
3. Solve for $ m $.

Multiplying both sides by 6:
$$ 6 \left( \frac{m}{3} - 3 \right) < 6 \left( \frac{4}{3} - \frac{m}{2} \right) $$

Simplifying:
$$ 2m - 18 < 8 - 3m $$

Now, we'll gather like terms and solve for $ m $:

$$ 2m + 3m < 8 + 18 $$
$$ 5m < 26 $$

Finally, divide both sides by 5 to isolate $ m $:
$$ m < \frac{26}{5} $$

So, the solution to the inequality $ \frac{m}{3} - 3 < \frac{4}{3} - \frac{m}{2} $ is $ m < \frac{26}{5} $.

How do you solve #\frac { m } { 3} - 3&lt; \frac { 4} { 3} - \frac { m } { 2}#?

How do you solve #\frac { m } { 3} - 3< \frac { 4} { 3} - \frac { m } { 2}#?