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

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

Solve for x

$$x\geq 7$$

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.

$$3\left(x+3\right)\leq 5\left(2x-5\right)-15$$

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

$$3x+9\leq 5\left(2x-5\right)-15$$

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

$$3x+9\leq 10x-25-15$$

Subtract 15 from -25 to get -40.

$$3x+9\leq 10x-40$$

Subtract 10x from both sides.

$$3x+9-10x\leq -40$$

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

$$-7x+9\leq -40$$

Subtract 9 from both sides.

$$-7x\leq -40-9$$

Subtract 9 from -40 to get -49.

$$-7x\leq -49$$

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

$$x\geq \frac{-49}{-7}$$

Divide -49 by -7 to get 7.

$$x\geq 7$$