Solve 2(2t-3)leq23(t-1)

$$2 ( 2 t - 3 ) \leq 23 ( t - 1 )$$

Solve for t

$$t\geq \frac{17}{19}$$

Solution Steps

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

$$4t-6\leq 23\left(t-1\right)$$

Use the distributive property to multiply 23 by t-1.

$$4t-6\leq 23t-23$$

Subtract 23t from both sides.

$$4t-6-23t\leq -23$$

Combine 4t and -23t to get -19t.

$$-19t-6\leq -23$$

Add 6 to both sides.

$$-19t\leq -23+6$$

Add -23 and 6 to get -17.

$$-19t\leq -17$$

Divide both sides by -19. Since -19 is negative, the inequality direction is changed.

$$t\geq \frac{-17}{-19}$$

Fraction \frac{-17}{-19} can be simplified to \frac{17}{19} by removing the negative sign from both the numerator and the denominator.

$$t\geq \frac{17}{19}$$