How to solve 2/3 imes+5=1/5-2x

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 2/3\times+5=1/5-2x | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$2/3 \times +5=1/5-2x$$

Solve for x

$x = -\frac{47}{30} = -1\frac{17}{30} \approx -1.566666667$

Steps for Solving Linear Equation

Express $\frac{2}{3}\times 5$ as a single fraction.

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

Multiply $2$ and $5$ to get $10$.

$$\frac{10}{3}=\frac{1}{5}-2x$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{5}-2x=\frac{10}{3}$$

Subtract $\frac{1}{5}$ from both sides.

$$-2x=\frac{10}{3}-\frac{1}{5}$$

Least common multiple of $3$ and $5$ is $15$. Convert $\frac{10}{3}$ and $\frac{1}{5}$ to fractions with denominator $15$.

$$-2x=\frac{50}{15}-\frac{3}{15}$$

Since $\frac{50}{15}$ and $\frac{3}{15}$ have the same denominator, subtract them by subtracting their numerators.

$$-2x=\frac{50-3}{15}$$

Subtract $3$ from $50$ to get $47$.

$$-2x=\frac{47}{15}$$

Divide both sides by $-2$.

$$x=\frac{\frac{47}{15}}{-2}$$

Express $\frac{\frac{47}{15}}{-2}$ as a single fraction.

$$x=\frac{47}{15\left(-2\right)}$$

Multiply $15$ and $-2$ to get $-30$.

$$x=\frac{47}{-30}$$

Fraction $\frac{47}{-30}$ can be rewritten as $-\frac{47}{30}$ by extracting the negative sign.

$$x=-\frac{47}{30}$$

Show Solution