Solve the Inequality for d 3(2d-1)>=4(2d-3)-3

$3 (2 d - 1) \geq 4 (2 d - 3) - 3$

Simplify $3 (2 d - 1)$ .

Rewrite.

$0 + 0 + 3 (2 d - 1) \geq 4 (2 d - 3) - 3$

Simplify by adding zeros.

$3 (2 d - 1) \geq 4 (2 d - 3) - 3$

Apply the distributive property.

$3 (2 d) + 3 \cdot - 1 \geq 4 (2 d - 3) - 3$

Multiply.

Multiply $2$ by $3$ .

$6 d + 3 \cdot - 1 \geq 4 (2 d - 3) - 3$

Multiply $3$ by $- 1$ .

$6 d - 3 \geq 4 (2 d - 3) - 3$

Simplify $4 (2 d - 3) - 3$ .

Simplify each term.

Apply the distributive property.

$6 d - 3 \geq 4 (2 d) + 4 \cdot - 3 - 3$

Multiply $2$ by $4$ .

$6 d - 3 \geq 8 d + 4 \cdot - 3 - 3$

Multiply $4$ by $- 3$ .

$6 d - 3 \geq 8 d - 12 - 3$

Subtract $3$ from $- 12$ .

$6 d - 3 \geq 8 d - 15$

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

Subtract $8 d$ from both sides of the inequality.

$6 d - 3 - 8 d \geq - 15$

Subtract $8 d$ from $6 d$ .

$- 2 d - 3 \geq - 15$

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

Add $3$ to both sides of the inequality.

$- 2 d \geq - 15 + 3$

Add $- 15$ and $3$ .

$- 2 d \geq - 12$

Divide each term in $- 2 d \geq - 12$ by $- 2$ and simplify.

Divide each term in $- 2 d \geq - 12$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 d}{- 2} \leq \frac{- 12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 d}{- 2} \leq \frac{- 12}{- 2}$

Divide $d$ by $1$ .

$d \leq \frac{- 12}{- 2}$

Simplify the right side.

Divide $- 12$ by $- 2$ .

$d \leq 6$

The result can be shown in multiple forms.

Inequality Form:

$d \leq 6$

Interval Notation:

$(- \infty, 6]$

Solve the Inequality for d 3(2d-1)>=4(2d-3)-3

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