Solve 3-x/3leq2(x-1)

$$\frac { 3 - x } { 3 } \leq 2 ( x - 1 )$$

Solve for x

$$x\geq \frac{9}{7}$$

Solution Steps

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$3-x\leq 6\left(x-1\right)$$

Use the distributive property to multiply 6 by x-1.

$$3-x\leq 6x-6$$

Subtract 6x from both sides.

$$3-x-6x\leq -6$$

Combine -x and -6x to get -7x.

$$3-7x\leq -6$$

Subtract 3 from both sides.

$$-7x\leq -6-3$$

Subtract 3 from -6 to get -9.

$$-7x\leq -9$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x\geq \frac{-9}{-7}$$

Fraction \frac{-9}{-7} can be simplified to \frac{9}{7} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{9}{7}$$