Solve -2x-3/5leq3left(4x-1right)/2

$$- \frac{ 2x-3 }{ 5 } \leq \frac{ 3 \left( 4x-1 \right) }{ 2 }$$

Solve for x

$$x\geq \frac{21}{64}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,2. Since 10 is positive, the inequality direction remains the same.

$$-2\left(2x-3\right)\leq 5\times 3\left(4x-1\right)$$

Use the distributive property to multiply -2 by 2x-3.

$$-4x+6\leq 5\times 3\left(4x-1\right)$$

Multiply 5 and 3 to get 15.

$$-4x+6\leq 15\left(4x-1\right)$$

Use the distributive property to multiply 15 by 4x-1.

$$-4x+6\leq 60x-15$$

Subtract 60x from both sides.

$$-4x+6-60x\leq -15$$

Combine -4x and -60x to get -64x.

$$-64x+6\leq -15$$

Subtract 6 from both sides.

$$-64x\leq -15-6$$

Subtract 6 from -15 to get -21.

$$-64x\leq -21$$

Divide both sides by -64. Since -64 is negative, the inequality direction is changed.

$$x\geq \frac{-21}{-64}$$

Fraction \frac{-21}{-64} can be simplified to \frac{21}{64} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{21}{64}$$