Solve 4(x-7)/9=5(x-3)/6

$$\frac { 4 ( x - 7 ) } { 9 } = \frac { 5 ( x - 3 ) } { 6 }$$

Solve for x

$$x = -\frac{11}{7} = -1\frac{4}{7} \approx -1.571428571$$

Steps for Solving Linear Equation

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

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

Multiply 2 and 4 to get 8.

$$8\left(x-7\right)=3\times 5\left(x-3\right)$$

Use the distributive property to multiply 8 by x-7.

$$8x-56=3\times 5\left(x-3\right)$$

Multiply 3 and 5 to get 15.

$$8x-56=15\left(x-3\right)$$

Use the distributive property to multiply 15 by x-3.

$$8x-56=15x-45$$

Subtract 15x from both sides.

$$8x-56-15x=-45$$

Combine 8x and -15x to get -7x.

$$-7x-56=-45$$

Add 56 to both sides.

$$-7x=-45+56$$

Add -45 and 56 to get 11.

$$-7x=11$$

Divide both sides by -7.

$$x=\frac{11}{-7}$$

Fraction \frac{11}{-7} can be rewritten as -\frac{11}{7} by extracting the negative sign.

$$x=-\frac{11}{7}$$