Solve 2left(-1+xright)/3geq3left(2x+3right)/4

$$\frac{ 2 \left( -1+x \right) }{ 3 } \geq \frac{ 3 \left( 2x+3 \right) }{ 4 }$$

Solve for x

$$x\leq -\frac{7}{2}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,4. Since 12 is positive, the inequality direction remains the same.

$$4\times 2\left(-1+x\right)\geq 3\times 3\left(2x+3\right)$$

Multiply 4 and 2 to get 8.

$$8\left(-1+x\right)\geq 3\times 3\left(2x+3\right)$$

Use the distributive property to multiply 8 by -1+x.

$$-8+8x\geq 3\times 3\left(2x+3\right)$$

Multiply 3 and 3 to get 9.

$$-8+8x\geq 9\left(2x+3\right)$$

Use the distributive property to multiply 9 by 2x+3.

$$-8+8x\geq 18x+27$$

Subtract 18x from both sides.

$$-8+8x-18x\geq 27$$

Combine 8x and -18x to get -10x.

$$-8-10x\geq 27$$

Add 8 to both sides.

$$-10x\geq 27+8$$

Add 27 and 8 to get 35.

$$-10x\geq 35$$

Divide both sides by -10. Since -10 is negative, the inequality direction is changed.

$$x\leq \frac{35}{-10}$$

Reduce the fraction \frac{35}{-10} to lowest terms by extracting and canceling out 5.

$$x\leq -\frac{7}{2}$$