Solve 5(x/5+10/2)geq2x+30/5

$$5 ( \frac { x } { 5 } + \frac { 10 } { 2 } ) \geq 2 x + \frac { 30 } { 5 }$$

Solve for x

$$x\leq 19$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,2. Since 10 is positive, the inequality direction remains the same.

$$50\left(\frac{x}{5}+\frac{10}{2}\right)\geq 20x+2\times 30$$

Divide 10 by 2 to get 5.

$$50\left(\frac{x}{5}+5\right)\geq 20x+2\times 30$$

Use the distributive property to multiply 50 by \frac{x}{5}+5.

$$50\times \frac{x}{5}+250\geq 20x+2\times 30$$

Cancel out 5, the greatest common factor in 50 and 5.

$$10x+250\geq 20x+2\times 30$$

Multiply 2 and 30 to get 60.

$$10x+250\geq 20x+60$$

Subtract 20x from both sides.

$$10x+250-20x\geq 60$$

Combine 10x and -20x to get -10x.

$$-10x+250\geq 60$$

Subtract 250 from both sides.

$$-10x\geq 60-250$$

Subtract 250 from 60 to get -190.

$$-10x\geq -190$$

Divide both sides by -10. Since -10 is negative, the inequality direction is changed.

$$x\leq \frac{-190}{-10}$$

Divide -190 by -10 to get 19.

$$x\leq 19$$