Solve x = 8; (3t - 2)/4 - (2t + 3)/3 = 2/3 - t | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$x=8; \frac{3t-2}{4}-\frac{2t+3}{3}=\frac{2}{3}-t$$

Solve for x, t

$x=8$
$t=2$

Solution Steps

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

$$3\left(3t-2\right)-4\left(2t+3\right)=8-12t$$

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

$$9t-6-4\left(2t+3\right)=8-12t$$

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

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

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

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

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

$$t-18=8-12t$$

Add $12t$ to both sides.

$$t-18+12t=8$$

Combine $t$ and $12t$ to get $13t$.

$$13t-18=8$$

Add $18$ to both sides.

$$13t=8+18$$

Add $8$ and $18$ to get $26$.

$$13t=26$$

Divide both sides by $13$.

$$t=\frac{26}{13}$$

Divide $26$ by $13$ to get $2$.

$$t=2$$

The system is now solved.

$$x=8$$ $$t=2$$