Solve the Inequality for x -6(4-x)<=-4(x+1)

$- 6 (4 - x) \leq - 4 (x + 1)$

Step 1

Simplify $- 6 (4 - x)$ .

Start simplifying.

$0 + 0 - 6 (4 - x) \leq - 4 (x + 1)$

Simplify by adding zeros.

$- 6 (4 - x) \leq - 4 (x + 1)$

Apply the distributive property.

$- 6 \cdot 4 - 6 (- x) \leq - 4 (x + 1)$

Multiply.

Multiply $- 6$ by $4$ .

$- 24 - 6 (- x) \leq - 4 (x + 1)$

Multiply $- 1$ by $- 6$ .

$- 24 + 6 x \leq - 4 (x + 1)$

Step 2

Simplify $- 4 (x + 1)$ .

Apply the distributive property.

$- 24 + 6 x \leq - 4 x - 4 \cdot 1$

Multiply $- 4$ by $1$ .

$- 24 + 6 x \leq - 4 x - 4$

Step 3

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

Add $4 x$ to both sides of the inequality.

$- 24 + 6 x + 4 x \leq - 4$

Add $6 x$ and $4 x$ .

$- 24 + 10 x \leq - 4$

Step 4

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

Add $24$ to both sides of the inequality.

$10 x \leq - 4 + 24$

Add $- 4$ and $24$ .

$10 x \leq 20$

Step 5

Divide each term in $10 x \leq 20$ by $10$ and simplify.

Divide each term in $10 x \leq 20$ by $10$ .

$\frac{10 x}{10} \leq \frac{20}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} \leq \frac{20}{10}$

Divide $x$ by $1$ .

$x \leq \frac{20}{10}$

Simplify the right side.

Divide $20$ by $10$ .

$x \leq 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \leq 2$

Interval Notation:

$(- \infty, 2]$

Solve the Inequality for x -6(4-x)<=-4(x+1)

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