Solve 3(t+2)/4=2(2t+3)/3

$$\frac { 3 ( t + 2 ) } { 4 } = \frac { 2 ( 2 t + 3 ) } { 3 }$$

Solve for t

$$t=-\frac{6}{7}\approx -0.857142857$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3.

$$3\times 3\left(t+2\right)=4\times 2\left(2t+3\right)$$

Multiply 3 and 3 to get 9.

$$9\left(t+2\right)=4\times 2\left(2t+3\right)$$

Use the distributive property to multiply 9 by t+2.

$$9t+18=4\times 2\left(2t+3\right)$$

Multiply 4 and 2 to get 8.

$$9t+18=8\left(2t+3\right)$$

Use the distributive property to multiply 8 by 2t+3.

$$9t+18=16t+24$$

Subtract 16t from both sides.

$$9t+18-16t=24$$

Combine 9t and -16t to get -7t.

$$-7t+18=24$$

Subtract 18 from both sides.

$$-7t=24-18$$

Subtract 18 from 24 to get 6.

$$-7t=6$$

Divide both sides by -7.

$$t=\frac{6}{-7}$$

Fraction \frac{6}{-7} can be rewritten as -\frac{6}{7} by extracting the negative sign.

$$t=-\frac{6}{7}$$