Solve for m 4m-5<m+2

$4 m - 5 < m + 2$

Step 1

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

Subtract $m$ from both sides of the inequality.

$4 m - 5 - m < 2$

Subtract $m$ from $4 m$ .

$3 m - 5 < 2$

Step 2

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

Add $5$ to both sides of the inequality.

$3 m < 2 + 5$

Add $2$ and $5$ .

$3 m < 7$

Step 3

Divide each term in $3 m < 7$ by $3$ and simplify.

Divide each term in $3 m < 7$ by $3$ .

$\frac{3 m}{3} < \frac{7}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 m}{3} < \frac{7}{3}$

Divide $m$ by $1$ .

$m < \frac{7}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$m < \frac{7}{3}$

Interval Notation:

$(- \infty, \frac{7}{3})$