Solve the Inequality for x -1.5(4x+1)>=4.5-2.5(x+1)

$- 1.5 (4 x + 1) \geq 4.5 - 2.5 (x + 1)$

Step 1

Simplify $- 1.5 (4 x + 1)$ .

Rewrite.

$0 + 0 - 1.5 (4 x + 1) \geq 4.5 - 2.5 (x + 1)$

Simplify by adding zeros.

$- 1.5 (4 x + 1) \geq 4.5 - 2.5 (x + 1)$

Apply the distributive property.

$- 1.5 (4 x) - 1.5 \cdot 1 \geq 4.5 - 2.5 (x + 1)$

Multiply.

Multiply $4$ by $- 1.5$ .

$- 6 x - 1.5 \cdot 1 \geq 4.5 - 2.5 (x + 1)$

Multiply $- 1.5$ by $1$ .

$- 6 x - 1.5 \geq 4.5 - 2.5 (x + 1)$

Step 2

Simplify $4.5 - 2.5 (x + 1)$ .

Simplify each term.

Apply the distributive property.

$- 6 x - 1.5 \geq 4.5 - 2.5 x - 2.5 \cdot 1$

Multiply $- 2.5$ by $1$ .

$- 6 x - 1.5 \geq 4.5 - 2.5 x - 2.5$

Subtract $2.5$ from $4.5$ .

$- 6 x - 1.5 \geq - 2.5 x + 2$

Step 3

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

Add $2.5 x$ to both sides of the inequality.

$- 6 x - 1.5 + 2.5 x \geq 2$

Add $- 6 x$ and $2.5 x$ .

$- 3.5 x - 1.5 \geq 2$

Step 4

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

Add $1.5$ to both sides of the inequality.

$- 3.5 x \geq 2 + 1.5$

Add $2$ and $1.5$ .

$- 3.5 x \geq 3.5$

Step 5

Divide each term in $- 3.5 x \geq 3.5$ by $- 3.5$ and simplify.

Divide each term in $- 3.5 x \geq 3.5$ by $- 3.5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3.5 x}{- 3.5} \leq \frac{3.5}{- 3.5}$

Simplify the left side.

Cancel the common factor of $- 3.5$ .

Cancel the common factor.

$\frac{- 3.5 x}{- 3.5} \leq \frac{3.5}{- 3.5}$

Divide $x$ by $1$ .

$x \leq \frac{3.5}{- 3.5}$

Simplify the right side.

Divide $3.5$ by $- 3.5$ .

$x \leq - 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 1$

Interval Notation:

$(- \infty, - 1]$

Solve the Inequality for x -1.5(4x+1)>=4.5-2.5(x+1)

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