Solve (2x+5)div(5x+1)=0.5

$$(2x+5) \div (5x+1)=0.5$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by 5x+1.

$$2x+5=0.5\left(5x+1\right)$$

Use the distributive property to multiply 0.5 by 5x+1.

$$2x+5=2.5x+0.5$$

Subtract 2.5x from both sides.

$$2x+5-2.5x=0.5$$

Combine 2x and -2.5x to get -0.5x.

$$-0.5x+5=0.5$$

Subtract 5 from both sides.

$$-0.5x=0.5-5$$

Subtract 5 from 0.5 to get -4.5.

$$-0.5x=-4.5$$

Divide both sides by -0.5.

$$x=\frac{-4.5}{-0.5}$$

Expand \frac{-4.5}{-0.5} by multiplying both numerator and the denominator by 10.

$$x=\frac{-45}{-5}$$

Divide -45 by -5 to get 9.

$$x=9$$