Solve f(2a+3)-(4a-8)=7?

$$f ( 2 a + 3 ) - ( 4 a - 8 ) = 7 ?$$

Solve for a

$$a=-\frac{3f+1}{2\left(f-2\right)}$$

$$f\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by 2a+3.

$$2fa+3f-\left(4a-8\right)=7$$

To find the opposite of 4a-8, find the opposite of each term.

$$2fa+3f-4a+8=7$$

Subtract 3f from both sides.

$$2fa-4a+8=7-3f$$

Subtract 8 from both sides.

$$2fa-4a=7-3f-8$$

Subtract 8 from 7 to get -1.

$$2fa-4a=-1-3f$$

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by 2f-4.

$$\frac{\left(2f-4\right)a}{2f-4}=\frac{-3f-1}{2f-4}$$

Dividing by 2f-4 undoes the multiplication by 2f-4.

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

Divide -1-3f by 2f-4.

$$a=-\frac{3f+1}{2\left(f-2\right)}$$

Solve for f

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

$$a\neq -\frac{3}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by 2a+3.

$$2fa+3f-\left(4a-8\right)=7$$

To find the opposite of 4a-8, find the opposite of each term.

$$2fa+3f-4a+8=7$$

Add 4a to both sides.

$$2fa+3f+8=7+4a$$

Subtract 8 from both sides.

$$2fa+3f=7+4a-8$$

Subtract 8 from 7 to get -1.

$$2fa+3f=-1+4a$$

Combine all terms containing f.

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

The equation is in standard form.

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

Divide both sides by 2a+3.

$$\frac{\left(2a+3\right)f}{2a+3}=\frac{4a-1}{2a+3}$$

Dividing by 2a+3 undoes the multiplication by 2a+3.

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