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

$$5 x - 2 - ( 2 x - 7 ) = 2 ( 3 x - 1 ) + \frac { 7 } { 2 }$$

Solve for x

$x = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$

Steps for Solving Linear Equation

To find the opposite of $2x-7$, find the opposite of each term.

$$5x-2-2x-\left(-7\right)=2\left(3x-1\right)+\frac{7}{2}$$

The opposite of $-7$ is $7$.

$$5x-2-2x+7=2\left(3x-1\right)+\frac{7}{2}$$

Combine $5x$ and $-2x$ to get $3x$.

$$3x-2+7=2\left(3x-1\right)+\frac{7}{2}$$

Add $-2$ and $7$ to get $5$.

$$3x+5=2\left(3x-1\right)+\frac{7}{2}$$

Use the distributive property to multiply $2$ by $3x-1$.

$$3x+5=6x-2+\frac{7}{2}$$

Convert $-2$ to fraction $-\frac{4}{2}$.

$$3x+5=6x-\frac{4}{2}+\frac{7}{2}$$

Since $-\frac{4}{2}$ and $\frac{7}{2}$ have the same denominator, add them by adding their numerators.

$$3x+5=6x+\frac{-4+7}{2}$$

Add $-4$ and $7$ to get $3$.

$$3x+5=6x+\frac{3}{2}$$

Subtract $6x$ from both sides.

$$3x+5-6x=\frac{3}{2}$$

Combine $3x$ and $-6x$ to get $-3x$.

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

Subtract $5$ from both sides.

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

Convert $5$ to fraction $\frac{10}{2}$.

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

Since $\frac{3}{2}$ and $\frac{10}{2}$ have the same denominator, subtract them by subtracting their numerators.

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

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

$$-3x=-\frac{7}{2}$$

Divide both sides by $-3$.

$$x=\frac{-\frac{7}{2}}{-3}$$

Express $\frac{-\frac{7}{2}}{-3}$ as a single fraction.

$$x=\frac{-7}{2\left(-3\right)}$$

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

$$x=\frac{-7}{-6}$$

Fraction $\frac{-7}{-6}$ can be simplified to $\frac{7}{6}$ by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7}{6}$$

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