Solve a+1/2-4a+1/3=4

$$\frac { a + 1 } { 2 } - \frac { 4 a + 1 } { 3 } = 4$$

Solve for a

$$a = -\frac{23}{5} = -4\frac{3}{5} = -4.6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(a+1\right)-2\left(4a+1\right)=24$$

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

$$3a+3-2\left(4a+1\right)=24$$

Use the distributive property to multiply -2 by 4a+1.

$$3a+3-8a-2=24$$

Combine 3a and -8a to get -5a.

$$-5a+3-2=24$$

Subtract 2 from 3 to get 1.

$$-5a+1=24$$

Subtract 1 from both sides.

$$-5a=24-1$$

Subtract 1 from 24 to get 23.

$$-5a=23$$

Divide both sides by -5.

$$a=\frac{23}{-5}$$

Fraction \frac{23}{-5} can be rewritten as -\frac{23}{5} by extracting the negative sign.

$$a=-\frac{23}{5}$$