How to solve x = 9/2 * [x - 3]

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 x = 9/2 * [x - 3] | Equatix

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Question

$$x=\frac{9}{2}[x-3]$$

Solve for x

$x = \frac{27}{7} = 3\frac{6}{7} \approx 3.857142857$

Steps for Solving Linear Equation

Use the distributive property to multiply $\frac{9}{2}$ by $x-3$.

$$x=\frac{9}{2}x+\frac{9}{2}\left(-3\right)$$

Express $\frac{9}{2}\left(-3\right)$ as a single fraction.

$$x=\frac{9}{2}x+\frac{9\left(-3\right)}{2}$$

Multiply $9$ and $-3$ to get $-27$.

$$x=\frac{9}{2}x+\frac{-27}{2}$$

Fraction $\frac{-27}{2}$ can be rewritten as $-\frac{27}{2}$ by extracting the negative sign.

$$x=\frac{9}{2}x-\frac{27}{2}$$

Subtract $\frac{9}{2}x$ from both sides.

$$x-\frac{9}{2}x=-\frac{27}{2}$$

Combine $x$ and $-\frac{9}{2}x$ to get $-\frac{7}{2}x$.

$$-\frac{7}{2}x=-\frac{27}{2}$$

Multiply both sides by $-\frac{2}{7}$, the reciprocal of $-\frac{7}{2}$.

$$x=-\frac{27}{2}\left(-\frac{2}{7}\right)$$

Multiply $-\frac{27}{2}$ times $-\frac{2}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-27\left(-2\right)}{2\times 7}$$

Do the multiplications in the fraction $\frac{-27\left(-2\right)}{2\times 7}$.

$$x=\frac{54}{14}$$

Reduce the fraction $\frac{54}{14}$ to lowest terms by extracting and canceling out $2$.

$$x=\frac{27}{7}$$

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