Solve 3(2t-2)/2>6t-3/5+t/10

$$\frac { 3 ( 2 t - 2 ) } { 2 } > \frac { 6 t - 3 } { 5 } + \frac { t } { 10 }$$

Solve for t

$$t>\frac{24}{17}$$

Solution Steps

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

$$5\times 3\left(2t-2\right)>2\left(6t-3\right)+t$$

Multiply 5 and 3 to get 15.

$$15\left(2t-2\right)>2\left(6t-3\right)+t$$

Use the distributive property to multiply 15 by 2t-2.

$$30t-30>2\left(6t-3\right)+t$$

Use the distributive property to multiply 2 by 6t-3.

$$30t-30>12t-6+t$$

Combine 12t and t to get 13t.

$$30t-30>13t-6$$

Subtract 13t from both sides.

$$30t-30-13t>-6$$

Combine 30t and -13t to get 17t.

$$17t-30>-6$$

Add 30 to both sides.

$$17t>-6+30$$

Add -6 and 30 to get 24.

$$17t>24$$

Divide both sides by 17. Since 17 is positive, the inequality direction remains the same.

$$t>\frac{24}{17}$$