Solve 2(2t-3)leq2.3(t-1)

$$2 ( 2 t - 3 ) \leq 2.3 ( t - 1 )$$

Solve for t

$$t\leq \frac{37}{17}$$

Solution Steps

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

$$4t-6\leq 2.3\left(t-1\right)$$

Use the distributive property to multiply 2.3 by t-1.

$$4t-6\leq 2.3t-2.3$$

Subtract 2.3t from both sides.

$$4t-6-2.3t\leq -2.3$$

Combine 4t and -2.3t to get 1.7t.

$$1.7t-6\leq -2.3$$

Add 6 to both sides.

$$1.7t\leq -2.3+6$$

Add -2.3 and 6 to get 3.7.

$$1.7t\leq 3.7$$

Divide both sides by 1.7. Since 1.7 is positive, the inequality direction remains the same.

$$t\leq \frac{3.7}{1.7}$$

Expand \frac{3.7}{1.7} by multiplying both numerator and the denominator by 10.

$$t\leq \frac{37}{17}$$