Solve 2^2/1x-14=2^-2/5*(2+0.5)

$$\frac{ { 2 }^{ 2 } }{ 1x-14 } = \frac{ { 2 }^{ -2 } }{ 5 \times (2+0.5) }$$

Solve for x

$$x=214$$

Steps for Solving Linear Equation

Variable x cannot be equal to 14 since division by zero is not defined. Multiply both sides of the equation by x-14.

$$2^{2}=\left(\frac{2}{25}x-\frac{28}{25}\right)\times 2^{-2}$$

Calculate 2 to the power of 2 and get 4.

$$4=\left(\frac{2}{25}x-\frac{28}{25}\right)\times 2^{-2}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$4=\left(\frac{2}{25}x-\frac{28}{25}\right)\times \frac{1}{4}$$

Use the distributive property to multiply \frac{2}{25}x-\frac{28}{25} by \frac{1}{4}.

$$4=\frac{1}{50}x-\frac{7}{25}$$

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

$$\frac{1}{50}x-\frac{7}{25}=4$$

Add \frac{7}{25} to both sides.

$$\frac{1}{50}x=4+\frac{7}{25}$$

Add 4 and \frac{7}{25} to get \frac{107}{25}.

$$\frac{1}{50}x=\frac{107}{25}$$

Multiply both sides by 50, the reciprocal of \frac{1}{50}.

$$x=\frac{107}{25}\times 50$$

Multiply \frac{107}{25} and 50 to get 214.

$$x=214$$