Solve the Inequality for d -1/4(d+1)<2

$- \frac{1}{4} (d + 1) < 2$

Step 1

Multiply each term in $- \frac{1}{4} \cdot (d + 1) < 2$ by $- 4$ to eliminate the fractions.

Multiply each term in $- \frac{1}{4} \cdot (d + 1) < 2$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{1}{4} \cdot (d + 1) \cdot - 4 > 2 \cdot - 4$

Simplify the left side.

Apply the distributive property.

$(- \frac{1}{4} d - \frac{1}{4} \cdot 1) \cdot - 4 > 2 \cdot - 4$

Combine $d$ and $\frac{1}{4}$ .

$(- \frac{d}{4} - \frac{1}{4} \cdot 1) \cdot - 4 > 2 \cdot - 4$

Multiply $- 1$ by $1$ .

$(- \frac{d}{4} - \frac{1}{4}) \cdot - 4 > 2 \cdot - 4$

Apply the distributive property.

$- \frac{d}{4} \cdot - 4 - \frac{1}{4} \cdot - 4 > 2 \cdot - 4$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{d}{4}$ into the numerator.

$\frac{- d}{4} \cdot - 4 - \frac{1}{4} \cdot - 4 > 2 \cdot - 4$

Factor $4$ out of $- 4$ .

$\frac{- d}{4} \cdot (4 (- 1)) - \frac{1}{4} \cdot - 4 > 2 \cdot - 4$

Cancel the common factor.

$\frac{- d}{4} \cdot (4 \cdot - 1) - \frac{1}{4} \cdot - 4 > 2 \cdot - 4$

Rewrite the expression.

$- d \cdot - 1 - \frac{1}{4} \cdot - 4 > 2 \cdot - 4$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 d - \frac{1}{4} \cdot - 4 > 2 \cdot - 4$

Multiply $d$ by $1$ .

$d - \frac{1}{4} \cdot - 4 > 2 \cdot - 4$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$d + \frac{- 1}{4} \cdot - 4 > 2 \cdot - 4$

Factor $4$ out of $- 4$ .

$d + \frac{- 1}{4} \cdot (4 (- 1)) > 2 \cdot - 4$

Cancel the common factor.

$d + \frac{- 1}{4} \cdot (4 \cdot - 1) > 2 \cdot - 4$

Rewrite the expression.

$d - 1 \cdot - 1 > 2 \cdot - 4$

Multiply $- 1$ by $- 1$ .

$d + 1 > 2 \cdot - 4$

Simplify the right side.

Multiply $2$ by $- 4$ .

$d + 1 > - 8$

Step 2

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

Subtract $1$ from both sides of the inequality.

$d > - 8 - 1$

Subtract $1$ from $- 8$ .

$d > - 9$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$d > - 9$

Interval Notation:

$(- 9, \infty)$

Solve the Inequality for d -1/4(d+1)<2

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