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

$$\frac { 1 } { 5 } ( 5 x - 1 ) = \frac { 1 } { 4 } ( 8 x + 1 )$$

Solve for x

$x=-\frac{9}{20}=-0.45$

Steps for Solving Linear Equation

Use the distributive property to multiply $\frac{1}{5}$ by $5x-1$.

$$\frac{1}{5}\times 5x+\frac{1}{5}\left(-1\right)=\frac{1}{4}\left(8x+1\right)$$

Cancel out $5$ and $5$.

$$x+\frac{1}{5}\left(-1\right)=\frac{1}{4}\left(8x+1\right)$$

Multiply $\frac{1}{5}$ and $-1$ to get $-\frac{1}{5}$.

$$x-\frac{1}{5}=\frac{1}{4}\left(8x+1\right)$$

Use the distributive property to multiply $\frac{1}{4}$ by $8x+1$.

$$x-\frac{1}{5}=\frac{1}{4}\times 8x+\frac{1}{4}$$

Multiply $\frac{1}{4}$ and $8$ to get $\frac{8}{4}$.

$$x-\frac{1}{5}=\frac{8}{4}x+\frac{1}{4}$$

Divide $8$ by $4$ to get $2$.

$$x-\frac{1}{5}=2x+\frac{1}{4}$$

Subtract $2x$ from both sides.

$$x-\frac{1}{5}-2x=\frac{1}{4}$$

Combine $x$ and $-2x$ to get $-x$.

$$-x-\frac{1}{5}=\frac{1}{4}$$

Add $\frac{1}{5}$ to both sides.

$$-x=\frac{1}{4}+\frac{1}{5}$$

Least common multiple of $4$ and $5$ is $20$. Convert $\frac{1}{4}$ and $\frac{1}{5}$ to fractions with denominator $20$.

$$-x=\frac{5}{20}+\frac{4}{20}$$

Since $\frac{5}{20}$ and $\frac{4}{20}$ have the same denominator, add them by adding their numerators.

$$-x=\frac{5+4}{20}$$

Add $5$ and $4$ to get $9$.

$$-x=\frac{9}{20}$$

Multiply both sides by $-1$.

$$x=-\frac{9}{20}$$

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