Solve the Inequality for d 1+3(-8d+1)>=10d+6+1

$1 + 3 (- 8 d + 1) \geq 10 d + 6 + 1$

Step 1

Simplify $1 + 3 (- 8 d + 1)$ .

Simplify each term.

Apply the distributive property.

$1 + 3 (- 8 d) + 3 \cdot 1 \geq 10 d + 6 + 1$

Multiply $- 8$ by $3$ .

$1 - 24 d + 3 \cdot 1 \geq 10 d + 6 + 1$

Multiply $3$ by $1$ .

$1 - 24 d + 3 \geq 10 d + 6 + 1$

Add $1$ and $3$ .

$- 24 d + 4 \geq 10 d + 6 + 1$

Step 2

Add $6$ and $1$ .

$- 24 d + 4 \geq 10 d + 7$

Step 3

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

Subtract $10 d$ from both sides of the inequality.

$- 24 d + 4 - 10 d \geq 7$

Subtract $10 d$ from $- 24 d$ .

$- 34 d + 4 \geq 7$

Step 4

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

Subtract $4$ from both sides of the inequality.

$- 34 d \geq 7 - 4$

Subtract $4$ from $7$ .

$- 34 d \geq 3$

Step 5

Divide each term in $- 34 d \geq 3$ by $- 34$ and simplify.

Divide each term in $- 34 d \geq 3$ by $- 34$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 34 d}{- 34} \leq \frac{3}{- 34}$

Simplify the left side.

Cancel the common factor of $- 34$ .

Cancel the common factor.

$\frac{- 34 d}{- 34} \leq \frac{3}{- 34}$

Divide $d$ by $1$ .

$d \leq \frac{3}{- 34}$

Simplify the right side.

Move the negative in front of the fraction.

$d \leq - \frac{3}{34}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$d \leq - \frac{3}{34}$

Interval Notation:

$(- \infty, - \frac{3}{34}]$

Solve the Inequality for d 1+3(-8d+1)>=10d+6+1

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