Solve the Inequality for x -30+5x>4(6+8x)

$- 30 + 5 x > 4 (6 + 8 x)$

Step 1

Simplify $4 (6 + 8 x)$ .

Rewrite.

$- 30 + 5 x > 0 + 0 + 4 (6 + 8 x)$

Simplify by adding zeros.

$- 30 + 5 x > 4 (6 + 8 x)$

Apply the distributive property.

$- 30 + 5 x > 4 \cdot 6 + 4 (8 x)$

Multiply.

Multiply $4$ by $6$ .

$- 30 + 5 x > 24 + 4 (8 x)$

Multiply $8$ by $4$ .

$- 30 + 5 x > 24 + 32 x$

Step 2

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

Subtract $32 x$ from both sides of the inequality.

$- 30 + 5 x - 32 x > 24$

Subtract $32 x$ from $5 x$ .

$- 30 - 27 x > 24$

Step 3

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

Add $30$ to both sides of the inequality.

$- 27 x > 24 + 30$

Add $24$ and $30$ .

$- 27 x > 54$

Step 4

Divide each term in $- 27 x > 54$ by $- 27$ and simplify.

Divide each term in $- 27 x > 54$ by $- 27$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 27 x}{- 27} < \frac{54}{- 27}$

Simplify the left side.

Cancel the common factor of $- 27$ .

Cancel the common factor.

$\frac{- 27 x}{- 27} < \frac{54}{- 27}$

Divide $x$ by $1$ .

$x < \frac{54}{- 27}$

Simplify the right side.

Divide $54$ by $- 27$ .

$x < - 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < - 2$

Interval Notation:

$(- \infty, - 2)$

Solve the Inequality for x -30+5x>4(6+8x)

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