Solve 4^2(x-5)=2.5(x-a)

$$4 ^ { 2 } ( x - 5 ) = 2.5 ( x - a )$$

Solve for a

$$a=-\frac{27x}{5}+32$$

Steps for Solving Linear Equation

Calculate 4 to the power of 2 and get 16.

$$16\left(x-5\right)=2.5\left(x-a\right)$$

Use the distributive property to multiply 16 by x-5.

$$16x-80=2.5\left(x-a\right)$$

Use the distributive property to multiply 2.5 by x-a.

$$16x-80=2.5x-2.5a$$

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

$$2.5x-2.5a=16x-80$$

Subtract 2.5x from both sides.

$$-2.5a=16x-80-2.5x$$

Combine 16x and -2.5x to get 13.5x.

$$-2.5a=13.5x-80$$

The equation is in standard form.

$$-2.5a=\frac{27x}{2}-80$$

Divide both sides of the equation by -2.5, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-2.5a}{-2.5}=\frac{\frac{27x}{2}-80}{-2.5}$$

Dividing by -2.5 undoes the multiplication by -2.5.

$$a=\frac{\frac{27x}{2}-80}{-2.5}$$

Divide \frac{27x}{2}-80 by -2.5 by multiplying \frac{27x}{2}-80 by the reciprocal of -2.5.

$$a=-\frac{27x}{5}+32$$

Solve for x

$$x=\frac{160-5a}{27}$$

Steps for Solving Linear Equation

Calculate 4 to the power of 2 and get 16.

$$16\left(x-5\right)=2.5\left(x-a\right)$$

Use the distributive property to multiply 16 by x-5.

$$16x-80=2.5\left(x-a\right)$$

Use the distributive property to multiply 2.5 by x-a.

$$16x-80=2.5x-2.5a$$

Subtract 2.5x from both sides.

$$16x-80-2.5x=-2.5a$$

Combine 16x and -2.5x to get 13.5x.

$$13.5x-80=-2.5a$$

Add 80 to both sides.

$$13.5x=-2.5a+80$$

The equation is in standard form.

$$13.5x=-\frac{5a}{2}+80$$

Divide both sides of the equation by 13.5, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{13.5x}{13.5}=\frac{-\frac{5a}{2}+80}{13.5}$$

Dividing by 13.5 undoes the multiplication by 13.5.

$$x=\frac{-\frac{5a}{2}+80}{13.5}$$

Divide -\frac{5a}{2}+80 by 13.5 by multiplying -\frac{5a}{2}+80 by the reciprocal of 13.5.

$$x=\frac{160-5a}{27}$$