How to solve 5 3 2x = 1/2

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.

Solve 5 3 2x = 1/2 | Equatix

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Question

$$\frac { 1 } { 5 } - \frac { 2 } { 3 } + 2 x = \frac { 1 } { 2 }$$

Solve for x

$x=\frac{29}{60}\approx 0.483333333$

Steps for Solving Linear Equation

Least common multiple of $5$ and $3$ is $15$. Convert $\frac{1}{5}$ and $\frac{2}{3}$ to fractions with denominator $15$.

$$\frac{3}{15}-\frac{10}{15}+2x=\frac{1}{2}$$

Since $\frac{3}{15}$ and $\frac{10}{15}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-10}{15}+2x=\frac{1}{2}$$

Subtract $10$ from $3$ to get $-7$.

$$-\frac{7}{15}+2x=\frac{1}{2}$$

Add $\frac{7}{15}$ to both sides.

$$2x=\frac{1}{2}+\frac{7}{15}$$

Least common multiple of $2$ and $15$ is $30$. Convert $\frac{1}{2}$ and $\frac{7}{15}$ to fractions with denominator $30$.

$$2x=\frac{15}{30}+\frac{14}{30}$$

Since $\frac{15}{30}$ and $\frac{14}{30}$ have the same denominator, add them by adding their numerators.

$$2x=\frac{15+14}{30}$$

Add $15$ and $14$ to get $29$.

$$2x=\frac{29}{30}$$

Divide both sides by $2$.

$$x=\frac{\frac{29}{30}}{2}$$

Express $\frac{\frac{29}{30}}{2}$ as a single fraction.

$$x=\frac{29}{30\times 2}$$

Multiply $30$ and $2$ to get $60$.

$$x=\frac{29}{60}$$

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