Math  /  Algebra

QuestionFind the solution set. m33>43m4\frac{m}{3}-3>\frac{4}{3}-\frac{m}{4}
The solution set is m>527m>\frac{52}{7}. (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in interval notation.)

Studdy Solution

STEP 1

1. We are given an inequality involving a variable m m .
2. The inequality is m33>43m4\frac{m}{3}-3>\frac{4}{3}-\frac{m}{4}.
3. We can solve the inequality by isolating the variable m m .

STEP 2

1. Eliminate the fractions by finding a common denominator.
2. Simplify the resulting expression.
3. Isolate the variable m m .
4. Express the solution in interval notation.

STEP 3

Identify the common denominator for the fractions.
The common denominator for m3 \frac{m}{3} and m4 \frac{m}{4} is 12.

STEP 4

Multiply every term by 12 to eliminate the fractions.
12(m33)>12(43m4) 12 \left(\frac{m}{3} - 3\right) > 12 \left(\frac{4}{3} - \frac{m}{4}\right)

STEP 5

Simplify the multiplied terms.
4m36>163m 4m - 36 > 16 - 3m

STEP 6

Add 3m 3m to both sides to begin isolating m m .
4m+3m36>16 4m + 3m - 36 > 16

STEP 7

Combine like terms.
7m36>16 7m - 36 > 16

STEP 8

Add 36 to both sides to further isolate m m .
7m>52 7m > 52

STEP 9

Divide both sides by 7.
m>527 m > \frac{52}{7}

STEP 10

Express the solution in interval notation.
m(527,) m \in \left(\frac{52}{7}, \infty\right)

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