Solve (xii) * (t + 12)/6 - t = 6 1/2 - 1/12 ( xiii ) | 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

$$( x i i ) \frac { t + 12 } { 6 } - t = 6 \frac { 1 } { 2 } - \frac { 1 } { 12 }$$

Solve for t

$t=-\frac{24i\xi -77}{2\left(i\xi -6\right)}$
$\xi \neq -6i$

Steps for Solving Linear Equation

Multiply both sides of the equation by $12$, the least common multiple of $6,2,12$.

$$2\xi i\left(t+12\right)-12t=6\left(6\times 2+1\right)-1$$

Multiply $2$ and $i$ to get $2i$.

$$2i\xi \left(t+12\right)-12t=6\left(6\times 2+1\right)-1$$

Use the distributive property to multiply $2i\xi $ by $t+12$.

$$2i\xi t+24i\xi -12t=6\left(6\times 2+1\right)-1$$

Multiply $6$ and $2$ to get $12$.

$$2i\xi t+24i\xi -12t=6\left(12+1\right)-1$$

Add $12$ and $1$ to get $13$.

$$2i\xi t+24i\xi -12t=6\times 13-1$$

Multiply $6$ and $13$ to get $78$.

$$2i\xi t+24i\xi -12t=78-1$$

Subtract $1$ from $78$ to get $77$.

$$2i\xi t+24i\xi -12t=77$$

Subtract $24i\xi $ from both sides.

$$2i\xi t-12t=77-24i\xi $$

Combine all terms containing $t$.

$$\left(2i\xi -12\right)t=77-24i\xi $$

Divide both sides by $2i\xi -12$.

$$\frac{\left(2i\xi -12\right)t}{2i\xi -12}=\frac{77-24i\xi }{2i\xi -12}$$

Dividing by $2i\xi -12$ undoes the multiplication by $2i\xi -12$.

$$t=\frac{77-24i\xi }{2i\xi -12}$$

Divide $77-24i\xi $ by $2i\xi -12$.

$$t=\frac{77-24i\xi }{2\left(i\xi -6\right)}$$

Solve for ξ

$\xi =\frac{12t+77}{2\left(it+12i\right)}$
$t\neq -12$

Steps for Solving Linear Equation

Multiply both sides of the equation by $12$, the least common multiple of $6,2,12$.

$$2\xi i\left(t+12\right)-12t=6\left(6\times 2+1\right)-1$$

Multiply $2$ and $i$ to get $2i$.

$$2i\xi \left(t+12\right)-12t=6\left(6\times 2+1\right)-1$$

Use the distributive property to multiply $2i\xi $ by $t+12$.

$$2i\xi t+24i\xi -12t=6\left(6\times 2+1\right)-1$$

Multiply $6$ and $2$ to get $12$.

$$2i\xi t+24i\xi -12t=6\left(12+1\right)-1$$

Add $12$ and $1$ to get $13$.

$$2i\xi t+24i\xi -12t=6\times 13-1$$

Multiply $6$ and $13$ to get $78$.

$$2i\xi t+24i\xi -12t=78-1$$

Subtract $1$ from $78$ to get $77$.

$$2i\xi t+24i\xi -12t=77$$

Add $12t$ to both sides.

$$2i\xi t+24i\xi =77+12t$$

Combine all terms containing $\xi $.

$$\left(2it+24i\right)\xi =77+12t$$

The equation is in standard form.

$$\left(2it+24i\right)\xi =12t+77$$

Divide both sides by $24i+2it$.

$$\frac{\left(2it+24i\right)\xi }{2it+24i}=\frac{12t+77}{2it+24i}$$

Dividing by $24i+2it$ undoes the multiplication by $24i+2it$.

$$\xi =\frac{12t+77}{2it+24i}$$

Divide $77+12t$ by $24i+2it$.

$$\xi =\frac{12t+77}{2\left(it+12i\right)}$$