Solve for d -23d+81<=-98d+1

$- 23 d + 81 \leq - 98 d + 1$

Step 1

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

Add $98 d$ to both sides of the inequality.

$- 23 d + 81 + 98 d \leq 1$

Add $- 23 d$ and $98 d$ .

$75 d + 81 \leq 1$

Step 2

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

Subtract $81$ from both sides of the inequality.

$75 d \leq 1 - 81$

Subtract $81$ from $1$ .

$75 d \leq - 80$

Step 3

Divide each term in $75 d \leq - 80$ by $75$ and simplify.

Divide each term in $75 d \leq - 80$ by $75$ .

$\frac{75 d}{75} \leq \frac{- 80}{75}$

Simplify the left side.

Cancel the common factor of $75$ .

Cancel the common factor.

$\frac{75 d}{75} \leq \frac{- 80}{75}$

Divide $d$ by $1$ .

$d \leq \frac{- 80}{75}$

Simplify the right side.

Cancel the common factor of $- 80$ and $75$ .

Factor $5$ out of $- 80$ .

$d \leq \frac{5 (- 16)}{75}$

Cancel the common factors.

Factor $5$ out of $75$ .

$d \leq \frac{5 \cdot - 16}{5 \cdot 15}$

Cancel the common factor.

$d \leq \frac{5 \cdot - 16}{5 \cdot 15}$

Rewrite the expression.

$d \leq \frac{- 16}{15}$

Move the negative in front of the fraction.

$d \leq - \frac{16}{15}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$d \leq - \frac{16}{15}$

Interval Notation:

$(- \infty, - \frac{16}{15}]$