Solve x+1/5leq2x-2/3=

$$\frac { x + 1 } { 5 } \leq \frac { 2 x - 2 } { 3 } =$$

Solve for x

$$x\geq \frac{13}{7}$$

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 5,3. Since 15 is positive, the inequality direction remains the same.

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

Use the distributive property to multiply 3 by x+1.

$$3x+3\leq 5\left(2x-2\right)$$

Use the distributive property to multiply 5 by 2x-2.

$$3x+3\leq 10x-10$$

Subtract 10x from both sides.

$$3x+3-10x\leq -10$$

Combine 3x and -10x to get -7x.

$$-7x+3\leq -10$$

Subtract 3 from both sides.

$$-7x\leq -10-3$$

Subtract 3 from -10 to get -13.

$$-7x\leq -13$$

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

$$x\geq \frac{-13}{-7}$$

Fraction \frac{-13}{-7} can be simplified to \frac{13}{7} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{13}{7}$$