Solve 2(x+4)/5=-3(x-2)/2

$$\frac { 2 ( x + 4 ) } { 5 } = \frac { - 3 ( x - 2 ) } { 2 }$$

Solve for x

$$x=\frac{14}{19}\approx 0.736842105$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 5,2.

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

Multiply 2 and 2 to get 4.

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

Use the distributive property to multiply 4 by x+4.

$$4x+16=5\left(-3\right)\left(x-2\right)$$

Multiply 5 and -3 to get -15.

$$4x+16=-15\left(x-2\right)$$

Use the distributive property to multiply -15 by x-2.

$$4x+16=-15x+30$$

Add 15x to both sides.

$$4x+16+15x=30$$

Combine 4x and 15x to get 19x.

$$19x+16=30$$

Subtract 16 from both sides.

$$19x=30-16$$

Subtract 16 from 30 to get 14.

$$19x=14$$

Divide both sides by 19.

$$x=\frac{14}{19}$$