Solve 5+2x/15leq1-x/10

$$\frac{ 5+2x }{ 15 } \leq \frac{ 1-x }{ 10 }$$

Solve for x

$$x\leq -1$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 15,10. Since 30 is positive, the inequality direction remains the same.

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

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

$$10+4x\leq 3\left(1-x\right)$$

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

$$10+4x\leq 3-3x$$

Add 3x to both sides.

$$10+4x+3x\leq 3$$

Combine 4x and 3x to get 7x.

$$10+7x\leq 3$$

Subtract 10 from both sides.

$$7x\leq 3-10$$

Subtract 10 from 3 to get -7.

$$7x\leq -7$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

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

Divide -7 by 7 to get -1.

$$x\leq -1$$