Solve 2 1/3 * (6/7 * m - 3) - 1 2/3 * (6/5 * m - 6) | 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

$$2\frac{1}{3}\cdot(\frac{6}{7}m-3)-1\frac{2}{3}\cdot(\frac{6}{5}m-6)$$

Evaluate

$3$

Solution Steps

Multiply $2$ and $3$ to get $6$.

$$\frac{6+1}{3}\left(\frac{6}{7}m-3\right)-\frac{1\times 3+2}{3}\left(\frac{6}{5}m-6\right)$$

Add $6$ and $1$ to get $7$.

$$\frac{7}{3}\left(\frac{6}{7}m-3\right)-\frac{1\times 3+2}{3}\left(\frac{6}{5}m-6\right)$$

Use the distributive property to multiply $\frac{7}{3}$ by $\frac{6}{7}m-3$.

$$\frac{7}{3}\times \frac{6}{7}m+\frac{7}{3}\left(-3\right)-\frac{1\times 3+2}{3}\left(\frac{6}{5}m-6\right)$$

Multiply $\frac{7}{3}$ times $\frac{6}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 6}{3\times 7}m+\frac{7}{3}\left(-3\right)-\frac{1\times 3+2}{3}\left(\frac{6}{5}m-6\right)$$

Cancel out $7$ in both numerator and denominator.

$$\frac{6}{3}m+\frac{7}{3}\left(-3\right)-\frac{1\times 3+2}{3}\left(\frac{6}{5}m-6\right)$$

Divide $6$ by $3$ to get $2$.

$$2m+\frac{7}{3}\left(-3\right)-\frac{1\times 3+2}{3}\left(\frac{6}{5}m-6\right)$$

Express $\frac{7}{3}\left(-3\right)$ as a single fraction.

$$2m+\frac{7\left(-3\right)}{3}-\frac{1\times 3+2}{3}\left(\frac{6}{5}m-6\right)$$

Multiply $7$ and $-3$ to get $-21$.

$$2m+\frac{-21}{3}-\frac{1\times 3+2}{3}\left(\frac{6}{5}m-6\right)$$

Divide $-21$ by $3$ to get $-7$.

$$2m-7-\frac{1\times 3+2}{3}\left(\frac{6}{5}m-6\right)$$

Multiply $1$ and $3$ to get $3$.

$$2m-7-\frac{3+2}{3}\left(\frac{6}{5}m-6\right)$$

Add $3$ and $2$ to get $5$.

$$2m-7-\frac{5}{3}\left(\frac{6}{5}m-6\right)$$

Use the distributive property to multiply $-\frac{5}{3}$ by $\frac{6}{5}m-6$.

$$2m-7-\frac{5}{3}\times \frac{6}{5}m-\frac{5}{3}\left(-6\right)$$

Multiply $-\frac{5}{3}$ times $\frac{6}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$2m-7+\frac{-5\times 6}{3\times 5}m-\frac{5}{3}\left(-6\right)$$

Do the multiplications in the fraction $\frac{-5\times 6}{3\times 5}$.

$$2m-7+\frac{-30}{15}m-\frac{5}{3}\left(-6\right)$$

Divide $-30$ by $15$ to get $-2$.

$$2m-7-2m-\frac{5}{3}\left(-6\right)$$

Express $-\frac{5}{3}\left(-6\right)$ as a single fraction.

$$2m-7-2m+\frac{-5\left(-6\right)}{3}$$

Multiply $-5$ and $-6$ to get $30$.

$$2m-7-2m+\frac{30}{3}$$

Divide $30$ by $3$ to get $10$.

$$2m-7-2m+10$$

Combine $2m$ and $-2m$ to get $0$.

$$-7+10$$

Add $-7$ and $10$ to get $3$.

$$3$$

Factor

$3$