1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

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

Solve for t

$t = -\frac{18}{7} = -2\frac{4}{7} \approx -2.571428571$

Steps for Solving Linear Equation

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

$$3\left(3t-2\right)-4\left(2t+3\right)=8t$$

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

$$9t-6-4\left(2t+3\right)=8t$$

Use the distributive property to multiply $-4$ by $2t+3$.

$$9t-6-8t-12=8t$$

Combine $9t$ and $-8t$ to get $t$.

$$t-6-12=8t$$

Subtract $12$ from $-6$ to get $-18$.

$$t-18=8t$$

Subtract $8t$ from both sides.

$$t-18-8t=0$$

Combine $t$ and $-8t$ to get $-7t$.

$$-7t-18=0$$

Add $18$ to both sides. Anything plus zero gives itself.

$$-7t=18$$

Divide both sides by $-7$.

$$t=\frac{18}{-7}$$

Fraction $\frac{18}{-7}$ can be rewritten as $-\frac{18}{7}$ by extracting the negative sign.

$$t=-\frac{18}{7}$$

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