Solve the Inequality for x 7x>1-4(1/4x+1)

$7 x > 1 - 4 (\frac{1}{4} x + 1)$

Step 1

Simplify $1 - 4 (\frac{1}{4} x + 1)$ .

Simplify each term.

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

$7 x > 1 - 4 (\frac{x}{4} + 1)$

Apply the distributive property.

$7 x > 1 - 4 \frac{x}{4} - 4 \cdot 1$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

$7 x > 1 + 4 (- 1) \frac{x}{4} - 4 \cdot 1$

Cancel the common factor.

$7 x > 1 + 4 \cdot - 1 \frac{x}{4} - 4 \cdot 1$

Rewrite the expression.

$7 x > 1 - 1 x - 4 \cdot 1$

Multiply $- 4$ by $1$ .

$7 x > 1 - 1 x - 4$

Rewrite $- 1 x$ as $- x$ .

$7 x > 1 - x - 4$

Subtract $4$ from $1$ .

$7 x > - x - 3$

Step 2

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

Add $x$ to both sides of the inequality.

$7 x + x > - 3$

Add $7 x$ and $x$ .

$8 x > - 3$

Step 3

Divide each term in $8 x > - 3$ by $8$ and simplify.

Divide each term in $8 x > - 3$ by $8$ .

$\frac{8 x}{8} > \frac{- 3}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} > \frac{- 3}{8}$

Divide $x$ by $1$ .

$x > \frac{- 3}{8}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{3}{8}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{3}{8}$

Interval Notation:

$(- \frac{3}{8}, \infty)$

Solve the Inequality for x 7x>1-4(1/4x+1)

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