Solve the Inequality for x (x-4)/3>=(x+3)/2

$\frac{x - 4}{3} \geq \frac{x + 3}{2}$

Step 1

Multiply both sides by $3$ .

$\frac{x - 4}{3} \cdot 3 \geq \frac{x + 3}{2} \cdot 3$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{x - 4}{3} \cdot 3 \geq \frac{x + 3}{2} \cdot 3$

Rewrite the expression.

$x - 4 \geq \frac{x + 3}{2} \cdot 3$

Simplify the right side.

Simplify $\frac{x + 3}{2} \cdot 3$ .

Combine $\frac{x + 3}{2}$ and $3$ .

$x - 4 \geq \frac{(x + 3) \cdot 3}{2}$

Move $3$ to the left of $x + 3$ .

$x - 4 \geq \frac{3 (x + 3)}{2}$

Step 3

Solve for $x$ .

Multiply both sides by $2$ .

$(x - 4) \cdot 2 \geq \frac{3 (x + 3)}{2} \cdot 2$

Simplify.

Simplify the left side.

Simplify $(x - 4) \cdot 2$ .

Apply the distributive property.

$x \cdot 2 - 4 \cdot 2 \geq \frac{3 (x + 3)}{2} \cdot 2$

Simplify the expression.

Move $2$ to the left of $x$ .

$2 \cdot x - 4 \cdot 2 \geq \frac{3 (x + 3)}{2} \cdot 2$

Multiply $- 4$ by $2$ .

$2 x - 8 \geq \frac{3 (x + 3)}{2} \cdot 2$

Simplify the right side.

Simplify $\frac{3 (x + 3)}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$2 x - 8 \geq \frac{3 (x + 3)}{2} \cdot 2$

Rewrite the expression.

$2 x - 8 \geq 3 (x + 3)$

Apply the distributive property.

$2 x - 8 \geq 3 x + 3 \cdot 3$

Multiply $3$ by $3$ .

$2 x - 8 \geq 3 x + 9$

Solve for $x$ .

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

Subtract $3 x$ from both sides of the inequality.

$2 x - 8 - 3 x \geq 9$

Subtract $3 x$ from $2 x$ .

$- x - 8 \geq 9$

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

Add $8$ to both sides of the inequality.

$- x \geq 9 + 8$

Add $9$ and $8$ .

$- x \geq 17$

Divide each term in $- x \geq 17$ by $- 1$ and simplify.

Divide each term in $- x \geq 17$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \leq \frac{17}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{17}{- 1}$

Divide $x$ by $1$ .

$x \leq \frac{17}{- 1}$

Simplify the right side.

Divide $17$ by $- 1$ .

$x \leq - 17$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 17$

Interval Notation:

$(- \infty, - 17]$

Solve the Inequality for x (x-4)/3>=(x+3)/2

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