Solve 2x-1/3-1geqx-5-3x/2

$$\frac { 2 x - 1 } { 3 } - 1 \geq x - \frac { 5 - 3 x } { 2 }$$

Solve for x

$$x\leq \frac{7}{11}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(2x-1\right)-6\geq 6x-3\left(5-3x\right)$$

Use the distributive property to multiply 2 by 2x-1.

$$4x-2-6\geq 6x-3\left(5-3x\right)$$

Subtract 6 from -2 to get -8.

$$4x-8\geq 6x-3\left(5-3x\right)$$

Use the distributive property to multiply -3 by 5-3x.

$$4x-8\geq 6x-15+9x$$

Combine 6x and 9x to get 15x.

$$4x-8\geq 15x-15$$

Subtract 15x from both sides.

$$4x-8-15x\geq -15$$

Combine 4x and -15x to get -11x.

$$-11x-8\geq -15$$

Add 8 to both sides.

$$-11x\geq -15+8$$

Add -15 and 8 to get -7.

$$-11x\geq -7$$

Divide both sides by -11. Since -11 is negative, the inequality direction is changed.

$$x\leq \frac{-7}{-11}$$

Fraction \frac{-7}{-11} can be simplified to \frac{7}{11} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{7}{11}$$