1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

$$- 1 \frac { 3 } { 5 } - ( 2 \frac { 2 } { 3 } - 4 \frac { 5 } { 6 } )$$

Evaluate

$\frac{17}{30}\approx 0.566666667$

Solution Steps

Multiply $1$ and $5$ to get $5$.

$$-\frac{5+3}{5}-\left(\frac{2\times 3+2}{3}-\frac{4\times 6+5}{6}\right)$$

Add $5$ and $3$ to get $8$.

$$-\frac{8}{5}-\left(\frac{2\times 3+2}{3}-\frac{4\times 6+5}{6}\right)$$

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

$$-\frac{8}{5}-\left(\frac{6+2}{3}-\frac{4\times 6+5}{6}\right)$$

Add $6$ and $2$ to get $8$.

$$-\frac{8}{5}-\left(\frac{8}{3}-\frac{4\times 6+5}{6}\right)$$

Multiply $4$ and $6$ to get $24$.

$$-\frac{8}{5}-\left(\frac{8}{3}-\frac{24+5}{6}\right)$$

Add $24$ and $5$ to get $29$.

$$-\frac{8}{5}-\left(\frac{8}{3}-\frac{29}{6}\right)$$

Least common multiple of $3$ and $6$ is $6$. Convert $\frac{8}{3}$ and $\frac{29}{6}$ to fractions with denominator $6$.

$$-\frac{8}{5}-\left(\frac{16}{6}-\frac{29}{6}\right)$$

Since $\frac{16}{6}$ and $\frac{29}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{8}{5}-\frac{16-29}{6}$$

Subtract $29$ from $16$ to get $-13$.

$$-\frac{8}{5}-\left(-\frac{13}{6}\right)$$

The opposite of $-\frac{13}{6}$ is $\frac{13}{6}$.

$$-\frac{8}{5}+\frac{13}{6}$$

Least common multiple of $5$ and $6$ is $30$. Convert $-\frac{8}{5}$ and $\frac{13}{6}$ to fractions with denominator $30$.

$$-\frac{48}{30}+\frac{65}{30}$$

Since $-\frac{48}{30}$ and $\frac{65}{30}$ have the same denominator, add them by adding their numerators.

$$\frac{-48+65}{30}$$

Add $-48$ and $65$ to get $17$.

$$\frac{17}{30}$$

Show Solution

Factor

$\frac{17}{2 \cdot 3 \cdot 5} = 0.5666666666666667$