How to solve 2t - 9 3t+4 -3 35

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.

Solve 2t - 9 3t+4 -3 35 | Equatix

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Question

$$\frac { 2 t - 4 } { 9 } = \frac { 3 t + 4 } { 3 } - \frac { - 3 } { 5 } + t$$

Solve for t

$t = -\frac{107}{80} = -1\frac{27}{80} = -1.3375$

Steps for Solving Linear Equation

Multiply both sides of the equation by $45$, the least common multiple of $9,3,5$.

$$5\left(2t-4\right)=15\left(3t+4\right)-9\left(-3\right)+45t$$

Use the distributive property to multiply $5$ by $2t-4$.

$$10t-20=15\left(3t+4\right)-9\left(-3\right)+45t$$

Use the distributive property to multiply $15$ by $3t+4$.

$$10t-20=45t+60-9\left(-3\right)+45t$$

Multiply $-9$ and $-3$ to get $27$.

$$10t-20=45t+60+27+45t$$

Add $60$ and $27$ to get $87$.

$$10t-20=45t+87+45t$$

Combine $45t$ and $45t$ to get $90t$.

$$10t-20=90t+87$$

Subtract $90t$ from both sides.

$$10t-20-90t=87$$

Combine $10t$ and $-90t$ to get $-80t$.

$$-80t-20=87$$

Add $20$ to both sides.

$$-80t=87+20$$

Add $87$ and $20$ to get $107$.

$$-80t=107$$

Divide both sides by $-80$.

$$t=\frac{107}{-80}$$

Fraction $\frac{107}{-80}$ can be rewritten as $-\frac{107}{80}$ by extracting the negative sign.

$$t=-\frac{107}{80}$$

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