Solve (3a+1)x/3=a(5x-3)/5

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

Solve for a

$$a=-\frac{5x}{9}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$5\left(3a+1\right)x=3a\left(5x-3\right)$$

Use the distributive property to multiply 5 by 3a+1.

$$\left(15a+5\right)x=3a\left(5x-3\right)$$

Use the distributive property to multiply 15a+5 by x.

$$15ax+5x=3a\left(5x-3\right)$$

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

$$15ax+5x=15ax-9a$$

Subtract 15ax from both sides.

$$15ax+5x-15ax=-9a$$

Combine 15ax and -15ax to get 0.

$$5x=-9a$$

Swap sides so that all variable terms are on the left hand side.

$$-9a=5x$$

Divide both sides by -9.

$$\frac{-9a}{-9}=\frac{5x}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$a=\frac{5x}{-9}$$

Divide 5x by -9.

$$a=-\frac{5x}{9}$$

Solve for x

$$x=-\frac{9a}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$5\left(3a+1\right)x=3a\left(5x-3\right)$$

Use the distributive property to multiply 5 by 3a+1.

$$\left(15a+5\right)x=3a\left(5x-3\right)$$

Use the distributive property to multiply 15a+5 by x.

$$15ax+5x=3a\left(5x-3\right)$$

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

$$15ax+5x=15xa-9a$$

Subtract 15xa from both sides.

$$15ax+5x-15xa=-9a$$

Combine 15ax and -15xa to get 0.

$$5x=-9a$$

Divide both sides by 5.

$$\frac{5x}{5}=-\frac{9a}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x=-\frac{9a}{5}$$