How to solve 2 7x3 2x - 9

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 7x3 2x - 9 | Equatix

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Question

$$\frac { 2 } { 7 x + 3 } = 2 \frac { 9 } { 2 x - 9 }$$

Solve for x

$x=-\frac{36}{61}\approx -0.590163934$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to any of the values $-\frac{3}{7},\frac{9}{2}$ since division by zero is not defined. Multiply both sides of the equation by $\left(2x-9\right)\left(7x+3\right)$, the least common multiple of $7x+3,2x-9$.

$$\left(2x-9\right)\times 2=2\left(7x+3\right)\times 9$$

Use the distributive property to multiply $2x-9$ by $2$.

$$4x-18=2\left(7x+3\right)\times 9$$

Multiply $2$ and $9$ to get $18$.

$$4x-18=18\left(7x+3\right)$$

Use the distributive property to multiply $18$ by $7x+3$.

$$4x-18=126x+54$$

Subtract $126x$ from both sides.

$$4x-18-126x=54$$

Combine $4x$ and $-126x$ to get $-122x$.

$$-122x-18=54$$

Add $18$ to both sides.

$$-122x=54+18$$

Add $54$ and $18$ to get $72$.

$$-122x=72$$

Divide both sides by $-122$.

$$x=\frac{72}{-122}$$

Reduce the fraction $\frac{72}{-122}$ to lowest terms by extracting and canceling out $2$.

$$x=-\frac{36}{61}$$

Show Solution