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

$$D = \frac { - \frac { 1 } { 5 } + \frac { 3 } { 2 } } { \frac { 4 } { 7 } - \frac { 5 } { 2 } }$$

Solve for D

$D=-\frac{91}{135}\approx -0.674074074$

Steps for Solving Linear Equation

Least common multiple of $5$ and $2$ is $10$. Convert $-\frac{1}{5}$ and $\frac{3}{2}$ to fractions with denominator $10$.

$$D=\frac{-\frac{2}{10}+\frac{15}{10}}{\frac{4}{7}-\frac{5}{2}}$$

Since $-\frac{2}{10}$ and $\frac{15}{10}$ have the same denominator, add them by adding their numerators.

$$D=\frac{\frac{-2+15}{10}}{\frac{4}{7}-\frac{5}{2}}$$

Add $-2$ and $15$ to get $13$.

$$D=\frac{\frac{13}{10}}{\frac{4}{7}-\frac{5}{2}}$$

Least common multiple of $7$ and $2$ is $14$. Convert $\frac{4}{7}$ and $\frac{5}{2}$ to fractions with denominator $14$.

$$D=\frac{\frac{13}{10}}{\frac{8}{14}-\frac{35}{14}}$$

Since $\frac{8}{14}$ and $\frac{35}{14}$ have the same denominator, subtract them by subtracting their numerators.

$$D=\frac{\frac{13}{10}}{\frac{8-35}{14}}$$

Subtract $35$ from $8$ to get $-27$.

$$D=\frac{\frac{13}{10}}{-\frac{27}{14}}$$

Divide $\frac{13}{10}$ by $-\frac{27}{14}$ by multiplying $\frac{13}{10}$ by the reciprocal of $-\frac{27}{14}$.

$$D=\frac{13}{10}\left(-\frac{14}{27}\right)$$

Multiply $\frac{13}{10}$ times $-\frac{14}{27}$ by multiplying numerator times numerator and denominator times denominator.

$$D=\frac{13\left(-14\right)}{10\times 27}$$

Do the multiplications in the fraction $\frac{13\left(-14\right)}{10\times 27}$.

$$D=\frac{-182}{270}$$

Reduce the fraction $\frac{-182}{270}$ to lowest terms by extracting and canceling out $2$.

$$D=-\frac{91}{135}$$

Show Solution

Assign D

$D≔-\frac{91}{135}$