Solve the Inequality for x -4(4+7x)+x>=-6x+5

$- 4 (4 + 7 x) + x \geq - 6 x + 5$

Step 1

Simplify $- 4 (4 + 7 x) + x$ .

Simplify each term.

Apply the distributive property.

$- 4 \cdot 4 - 4 (7 x) + x \geq - 6 x + 5$

Multiply $- 4$ by $4$ .

$- 16 - 4 (7 x) + x \geq - 6 x + 5$

Multiply $7$ by $- 4$ .

$- 16 - 28 x + x \geq - 6 x + 5$

Add $- 28 x$ and $x$ .

$- 16 - 27 x \geq - 6 x + 5$

Step 2

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

Add $6 x$ to both sides of the inequality.

$- 16 - 27 x + 6 x \geq 5$

Add $- 27 x$ and $6 x$ .

$- 16 - 21 x \geq 5$

Step 3

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

Add $16$ to both sides of the inequality.

$- 21 x \geq 5 + 16$

Add $5$ and $16$ .

$- 21 x \geq 21$

Step 4

Divide each term in $- 21 x \geq 21$ by $- 21$ and simplify.

Divide each term in $- 21 x \geq 21$ by $- 21$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 21 x}{- 21} \leq \frac{21}{- 21}$

Simplify the left side.

Cancel the common factor of $- 21$ .

Cancel the common factor.

$\frac{- 21 x}{- 21} \leq \frac{21}{- 21}$

Divide $x$ by $1$ .

$x \leq \frac{21}{- 21}$

Simplify the right side.

Divide $21$ by $- 21$ .

$x \leq - 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 1$

Interval Notation:

$(- \infty, - 1]$

Solve the Inequality for x -4(4+7x)+x>=-6x+5

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