Solve for x 3x-8>=4(x-1.5)

$3 x - 8 \geq 4 (x - 1.5)$

Step 1

Simplify $4 (x - 1.5)$ .

Rewrite.

$3 x - 8 \geq 0 + 0 + 4 (x - 1.5)$

Simplify by adding zeros.

$3 x - 8 \geq 4 (x - 1.5)$

Apply the distributive property.

$3 x - 8 \geq 4 x + 4 \cdot - 1.5$

Multiply $4$ by $- 1.5$ .

$3 x - 8 \geq 4 x - 6$

Step 2

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

Subtract $4 x$ from both sides of the inequality.

$3 x - 8 - 4 x \geq - 6$

Subtract $4 x$ from $3 x$ .

$- x - 8 \geq - 6$

Step 3

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

Add $8$ to both sides of the inequality.

$- x \geq - 6 + 8$

Add $- 6$ and $8$ .

$- x \geq 2$

Step 4

Divide each term in $- x \geq 2$ by $- 1$ and simplify.

Divide each term in $- x \geq 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \leq \frac{2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{2}{- 1}$

Divide $x$ by $1$ .

$x \leq \frac{2}{- 1}$

Simplify the right side.

Divide $2$ by $- 1$ .

$x \leq - 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 2$

Interval Notation:

$(- \infty, - 2]$

Solve for x 3x-8>=4(x-1.5)

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