Solve the Inequality for d 2d-3<=3d+7

$2 d - 3 \leq 3 d + 7$

Step 1

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

Subtract $3 d$ from both sides of the inequality.

$2 d - 3 - 3 d \leq 7$

Subtract $3 d$ from $2 d$ .

$- d - 3 \leq 7$

Step 2

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

Add $3$ to both sides of the inequality.

$- d \leq 7 + 3$

Add $7$ and $3$ .

$- d \leq 10$

Step 3

Divide each term in $- d \leq 10$ by $- 1$ and simplify.

Divide each term in $- d \leq 10$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- d}{- 1} \geq \frac{10}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{d}{1} \geq \frac{10}{- 1}$

Divide $d$ by $1$ .

$d \geq \frac{10}{- 1}$

Simplify the right side.

Divide $10$ by $- 1$ .

$d \geq - 10$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$d \geq - 10$

Interval Notation:

$[- 10, \infty)$

Solve the Inequality for d 2d-3<=3d+7

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