Solve 3a-7/4=4a+5/3

$$\frac { 3 a - 7 } { 4 } = \frac { 4 a + 5 } { 3 }$$

Solve for a

$$a = -\frac{41}{7} = -5\frac{6}{7} \approx -5.857142857$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3.

$$3\left(3a-7\right)=4\left(4a+5\right)$$

Use the distributive property to multiply 3 by 3a-7.

$$9a-21=4\left(4a+5\right)$$

Use the distributive property to multiply 4 by 4a+5.

$$9a-21=16a+20$$

Subtract 16a from both sides.

$$9a-21-16a=20$$

Combine 9a and -16a to get -7a.

$$-7a-21=20$$

Add 21 to both sides.

$$-7a=20+21$$

Add 20 and 21 to get 41.

$$-7a=41$$

Divide both sides by -7.

$$a=\frac{41}{-7}$$

Fraction \frac{41}{-7} can be rewritten as -\frac{41}{7} by extracting the negative sign.

$$a=-\frac{41}{7}$$