Solve the Inequality for D 15<=1.04D-34.6<=23

$15 \leq 1.04 D - 34.6 \leq 23$

Step 1

Move all terms not containing $D$ from the center section of the inequality.

Add $34.6$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$15 + 34.6 \leq 1.04 D \leq 23 + 34.6$

Add $15$ and $34.6$ .

$49.6 \leq 1.04 D \leq 23 + 34.6$

Add $23$ and $34.6$ .

$49.6 \leq 1.04 D \leq 57.6$

Step 2

Divide each term in the inequality by $1.04$ .

$\frac{49.6}{1.04} \leq \frac{1.04 D}{1.04} \leq \frac{57.6}{1.04}$

Step 3

Divide $49.6$ by $1.04$ .

$47.\overline{692307} \leq \frac{1.04 D}{1.04} \leq \frac{57.6}{1.04}$

Step 4

Cancel the common factor of $1.04$ .

Cancel the common factor.

$47.\overline{692307} \leq \frac{1.04 D}{1.04} \leq \frac{57.6}{1.04}$

Divide $D$ by $1$ .

$47.\overline{692307} \leq D \leq \frac{57.6}{1.04}$

Step 5

Divide $57.6$ by $1.04$ .

$47.\overline{692307} \leq D \leq 55.\overline{384615}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$47.\overline{692307} \leq D \leq 55.\overline{384615}$

Interval Notation:

$[47.\overline{692307}, 55.\overline{384615}]$

Step 7