Solve x+2/10-1leq1-x/4

$$\frac { x + 2 } { 10 } - 1 \leq \frac { 1 - x } { 4 }$$

Solve for x

$$x\leq 3$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 10,4. Since 20 is positive, the inequality direction remains the same.

$$2\left(x+2\right)-20\leq 5\left(1-x\right)$$

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

$$2x+4-20\leq 5\left(1-x\right)$$

Subtract 20 from 4 to get -16.

$$2x-16\leq 5\left(1-x\right)$$

Use the distributive property to multiply 5 by 1-x.

$$2x-16\leq 5-5x$$

Add 5x to both sides.

$$2x-16+5x\leq 5$$

Combine 2x and 5x to get 7x.

$$7x-16\leq 5$$

Add 16 to both sides.

$$7x\leq 5+16$$

Add 5 and 16 to get 21.

$$7x\leq 21$$

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

$$x\leq \frac{21}{7}$$

Divide 21 by 7 to get 3.

$$x\leq 3$$