Solve VERIFED5/2\times(7/2\times11/2)=(5/2\times7/5)\times11/3 | 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

$$VERIFED5/2 \times (7/2 \times 11/2)=(5/2 \times 7/5) \times 11/3$$

Solve for D_5

$D_{5}=\frac{4}{3FIRVE^{2}}$
$F\neq 0\text{ and }R\neq 0\text{ and }E\neq 0\text{ and }V\neq 0\text{ and }I\neq 0$

Steps for Solving Linear Equation

Multiply both sides of the equation by $6$, the least common multiple of $2,3$.

$$3VERIFED_{5}\times \frac{\frac{7}{2}\times 11}{2}=2\times \frac{\frac{5}{2}\times 7}{5}\times 11$$

Multiply $E$ and $E$ to get $E^{2}$.

$$3VE^{2}RIFD_{5}\times \frac{\frac{7}{2}\times 11}{2}=2\times \frac{\frac{5}{2}\times 7}{5}\times 11$$

Multiply $\frac{7}{2}$ and $11$ to get $\frac{77}{2}$.

$$3VE^{2}RIFD_{5}\times \frac{\frac{77}{2}}{2}=2\times \frac{\frac{5}{2}\times 7}{5}\times 11$$

Express $\frac{\frac{77}{2}}{2}$ as a single fraction.

$$3VE^{2}RIFD_{5}\times \frac{77}{2\times 2}=2\times \frac{\frac{5}{2}\times 7}{5}\times 11$$

Multiply $2$ and $2$ to get $4$.

$$3VE^{2}RIFD_{5}\times \frac{77}{4}=2\times \frac{\frac{5}{2}\times 7}{5}\times 11$$

Multiply $3$ and $\frac{77}{4}$ to get $\frac{231}{4}$.

$$\frac{231}{4}VE^{2}RIFD_{5}=2\times \frac{\frac{5}{2}\times 7}{5}\times 11$$

Multiply $\frac{5}{2}$ and $7$ to get $\frac{35}{2}$.

$$\frac{231}{4}VE^{2}RIFD_{5}=2\times \frac{\frac{35}{2}}{5}\times 11$$

Express $\frac{\frac{35}{2}}{5}$ as a single fraction.

$$\frac{231}{4}VE^{2}RIFD_{5}=2\times \frac{35}{2\times 5}\times 11$$

Multiply $2$ and $5$ to get $10$.

$$\frac{231}{4}VE^{2}RIFD_{5}=2\times \frac{35}{10}\times 11$$

Reduce the fraction $\frac{35}{10}$ to lowest terms by extracting and canceling out $5$.

$$\frac{231}{4}VE^{2}RIFD_{5}=2\times \frac{7}{2}\times 11$$

Multiply $2$ and $\frac{7}{2}$ to get $7$.

$$\frac{231}{4}VE^{2}RIFD_{5}=7\times 11$$

Multiply $7$ and $11$ to get $77$.

$$\frac{231}{4}VE^{2}RIFD_{5}=77$$

The equation is in standard form.

$$\frac{231FIRVE^{2}}{4}D_{5}=77$$

Divide both sides by $\frac{231}{4}VE^{2}RIF$.

$$\frac{4\times \frac{231FIRVE^{2}}{4}D_{5}}{231FIRVE^{2}}=\frac{4\times 77}{231FIRVE^{2}}$$

Dividing by $\frac{231}{4}VE^{2}RIF$ undoes the multiplication by $\frac{231}{4}VE^{2}RIF$.

$$D_{5}=\frac{4\times 77}{231FIRVE^{2}}$$

Divide $77$ by $\frac{231}{4}VE^{2}RIF$.

$$D_{5}=\frac{4}{3FIRVE^{2}}$$

Solve for E (complex solution)

$E=-\frac{2\sqrt{3}D_{5}^{-\frac{1}{2}}F^{-\frac{1}{2}}I^{-\frac{1}{2}}R^{-\frac{1}{2}}V^{-\frac{1}{2}}}{3}$
$E=\frac{2\sqrt{3}D_{5}^{-\frac{1}{2}}F^{-\frac{1}{2}}I^{-\frac{1}{2}}R^{-\frac{1}{2}}V^{-\frac{1}{2}}}{3}\text{, }D_{5}\neq 0\text{ and }F\neq 0\text{ and }R\neq 0\text{ and }V\neq 0\text{ and }I\neq 0$