Convert to Set Notation 7(3m-(m+2))>-6(m-3)

$7 (3 m - (m + 2)) > - 6 (m - 3)$

Step 1

Solve $m > \frac{8}{5}$ .

Simplify $7 (3 m - (m + 2))$ .

Rewrite.

$0 + 0 + 7 (3 m - (m + 2)) > - 6 (m - 3)$

Simplify by adding zeros.

$7 (3 m - (m + 2)) > - 6 (m - 3)$

Simplify each term.

Apply the distributive property.

$7 (3 m - m - 1 \cdot 2) > - 6 (m - 3)$

Multiply $- 1$ by $2$ .

$7 (3 m - m - 2) > - 6 (m - 3)$

Simplify terms.

Subtract $m$ from $3 m$ .

$7 (2 m - 2) > - 6 (m - 3)$

Apply the distributive property.

$7 (2 m) + 7 \cdot - 2 > - 6 (m - 3)$

Multiply.

Multiply $2$ by $7$ .

$14 m + 7 \cdot - 2 > - 6 (m - 3)$

Multiply $7$ by $- 2$ .

$14 m - 14 > - 6 (m - 3)$

Simplify $- 6 (m - 3)$ .

Apply the distributive property.

$14 m - 14 > - 6 m - 6 \cdot - 3$

Multiply $- 6$ by $- 3$ .

$14 m - 14 > - 6 m + 18$

Move all terms containing $m$ to the left side of the inequality.

Add $6 m$ to both sides of the inequality.

$14 m - 14 + 6 m > 18$

Add $14 m$ and $6 m$ .

$20 m - 14 > 18$

Move all terms not containing $m$ to the right side of the inequality.

Add $14$ to both sides of the inequality.

$20 m > 18 + 14$

Add $18$ and $14$ .

$20 m > 32$

Divide each term in $20 m > 32$ by $20$ and simplify.

Divide each term in $20 m > 32$ by $20$ .

$\frac{20 m}{20} > \frac{32}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 m}{20} > \frac{32}{20}$

Divide $m$ by $1$ .

$m > \frac{32}{20}$

Simplify the right side.

Cancel the common factor of $32$ and $20$ .

Factor $4$ out of $32$ .

$m > \frac{4 (8)}{20}$

Cancel the common factors.

Factor $4$ out of $20$ .

$m > \frac{4 \cdot 8}{4 \cdot 5}$

Cancel the common factor.

$m > \frac{4 \cdot 8}{4 \cdot 5}$

Rewrite the expression.

$m > \frac{8}{5}$

Step 2

Use the inequality $m > \frac{8}{5}$ to build the set notation.

${m | m > \frac{8}{5}}$

Step 3

Convert to Set Notation 7(3m-(m+2))>-6(m-3)

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