Solve x-2/2+0.5-2x-3/7+1/14leq0

$$\frac{ x-2 }{ 2 } +0.5- \frac{ 2x-3 }{ 7 } + \frac{ 1 }{ 14 } \leq 0$$

Solve for x

$$x\leq 0$$

Solution Steps

Multiply both sides of the equation by 14, the least common multiple of 2,7,14. Since 14 is positive, the inequality direction remains the same.

$$7\left(x-2\right)+7-2\left(2x-3\right)+1\leq 0$$

Use the distributive property to multiply 7 by x-2.

$$7x-14+7-2\left(2x-3\right)+1\leq 0$$

Add -14 and 7 to get -7.

$$7x-7-2\left(2x-3\right)+1\leq 0$$

Use the distributive property to multiply -2 by 2x-3.

$$7x-7-4x+6+1\leq 0$$

Combine 7x and -4x to get 3x.

$$3x-7+6+1\leq 0$$

Add -7 and 6 to get -1.

$$3x-1+1\leq 0$$

Add -1 and 1 to get 0.

$$3x\leq 0$$

Product of two numbers is ≤0 if one is ≥0 and the other is ≤0. Since 3\geq 0, x must be ≤0.

$$x\leq 0$$