Solve 2/(9 + 14) = 2/(ab) + 16/T_{7} | 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

$$\frac{2}{9+14}=\frac{2}{a\cdot b}+\frac{16}{T_{7}}$$

Solve for T_7

$T_{7}=-\frac{184ab}{23-ab}$
$b\neq 0\text{ and }a\neq 0\text{ and }a\neq \frac{23}{b}$

Steps for Solving Linear Equation

Variable $T_{7}$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $T_{7}ab$, the least common multiple of $ab,T_{7}$.

$$\frac{1}{23}T_{7}ab\times 2=T_{7}\times 2+ab\times 16$$

Multiply $\frac{1}{23}$ and $2$ to get $\frac{2}{23}$.

$$\frac{2}{23}T_{7}ab=T_{7}\times 2+ab\times 16$$

Subtract $T_{7}\times 2$ from both sides.

$$\frac{2}{23}T_{7}ab-T_{7}\times 2=ab\times 16$$

Multiply $-1$ and $2$ to get $-2$.

$$\frac{2}{23}T_{7}ab-2T_{7}=ab\times 16$$

Combine all terms containing $T_{7}$.

$$\left(\frac{2}{23}ab-2\right)T_{7}=ab\times 16$$

The equation is in standard form.

$$\left(\frac{2ab}{23}-2\right)T_{7}=16ab$$

Divide both sides by $\frac{2}{23}ab-2$.

$$\frac{\left(\frac{2ab}{23}-2\right)T_{7}}{\frac{2ab}{23}-2}=\frac{16ab}{\frac{2ab}{23}-2}$$

Dividing by $\frac{2}{23}ab-2$ undoes the multiplication by $\frac{2}{23}ab-2$.

$$T_{7}=\frac{16ab}{\frac{2ab}{23}-2}$$

Divide $16ab$ by $\frac{2}{23}ab-2$.

$$T_{7}=\frac{184ab}{ab-23}$$

Variable $T_{7}$ cannot be equal to $0$.

$$T_{7}=\frac{184ab}{ab-23}\text{, }T_{7}\neq 0$$

Solve for a

$a=-\frac{23T_{7}}{b\left(184-T_{7}\right)}$
$T_{7}\neq 0\text{ and }T_{7}\neq 184\text{ and }b\neq 0$

Steps for Solving Linear Equation

Variable $a$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $T_{7}ab$, the least common multiple of $ab,T_{7}$.

$$\frac{1}{23}T_{7}ab\times 2=T_{7}\times 2+ab\times 16$$

Multiply $\frac{1}{23}$ and $2$ to get $\frac{2}{23}$.

$$\frac{2}{23}T_{7}ab=T_{7}\times 2+ab\times 16$$

Subtract $ab\times 16$ from both sides.

$$\frac{2}{23}T_{7}ab-ab\times 16=T_{7}\times 2$$

Multiply $-1$ and $16$ to get $-16$.

$$\frac{2}{23}T_{7}ab-16ab=T_{7}\times 2$$

Combine all terms containing $a$.

$$\left(\frac{2}{23}T_{7}b-16b\right)a=T_{7}\times 2$$

The equation is in standard form.

$$\left(\frac{2T_{7}b}{23}-16b\right)a=2T_{7}$$

Divide both sides by $\frac{2}{23}T_{7}b-16b$.

$$\frac{\left(\frac{2T_{7}b}{23}-16b\right)a}{\frac{2T_{7}b}{23}-16b}=\frac{2T_{7}}{\frac{2T_{7}b}{23}-16b}$$

Dividing by $\frac{2}{23}T_{7}b-16b$ undoes the multiplication by $\frac{2}{23}T_{7}b-16b$.

$$a=\frac{2T_{7}}{\frac{2T_{7}b}{23}-16b}$$

Divide $2T_{7}$ by $\frac{2}{23}T_{7}b-16b$.

$$a=\frac{23T_{7}}{b\left(T_{7}-184\right)}$$

Variable $a$ cannot be equal to $0$.

$$a=\frac{23T_{7}}{b\left(T_{7}-184\right)}\text{, }a\neq 0$$