Solve 6/30+x-6/50leq1/2

$$\frac{ 6 }{ 30 } + \frac{ x-6 }{ 50 } \leq \frac{ 1 }{ 2 }$$

Solve for x

$$x\leq 21$$

Solution Steps

Multiply both sides of the equation by 150, the least common multiple of 30,50,2. Since 150 is positive, the inequality direction remains the same.

$$5\times 6+3\left(x-6\right)\leq 75$$

Multiply 5 and 6 to get 30.

$$30+3\left(x-6\right)\leq 75$$

Use the distributive property to multiply 3 by x-6.

$$30+3x-18\leq 75$$

Subtract 18 from 30 to get 12.

$$12+3x\leq 75$$

Subtract 12 from both sides.

$$3x\leq 75-12$$

Subtract 12 from 75 to get 63.

$$3x\leq 63$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x\leq \frac{63}{3}$$

Divide 63 by 3 to get 21.

$$x\leq 21$$