Solve 2x-5/6=4x-7/9

$$\frac { 2 x - 5 } { 6 } = \frac { 4 x - 7 } { 9 }$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18, the least common multiple of 6,9.

$$3\left(2x-5\right)=2\left(4x-7\right)$$

Use the distributive property to multiply 3 by 2x-5.

$$6x-15=2\left(4x-7\right)$$

Use the distributive property to multiply 2 by 4x-7.

$$6x-15=8x-14$$

Subtract 8x from both sides.

$$6x-15-8x=-14$$

Combine 6x and -8x to get -2x.

$$-2x-15=-14$$

Add 15 to both sides.

$$-2x=-14+15$$

Add -14 and 15 to get 1.

$$-2x=1$$

Divide both sides by -2.

$$x=\frac{1}{-2}$$

Fraction \frac{1}{-2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$x=-\frac{1}{2}$$