Solve 1/2(7x-2)+6x=37+r

$$\frac { 1 } { 2 } ( 7 x - 2 ) + 6 x = 37 + r$$

Solve for r

$$r=\frac{19\left(x-4\right)}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 7x-2.

$$\frac{7}{2}x-1+6x=37+r$$

Combine \frac{7}{2}x and 6x to get \frac{19}{2}x.

$$\frac{19}{2}x-1=37+r$$

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

$$37+r=\frac{19}{2}x-1$$

Subtract 37 from both sides.

$$r=\frac{19}{2}x-1-37$$

Subtract 37 from -1 to get -38.

$$r=\frac{19}{2}x-38$$

Solve for x

$$x=\frac{2\left(r+38\right)}{19}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by 7x-2.

$$\frac{7}{2}x-1+6x=37+r$$

Combine \frac{7}{2}x and 6x to get \frac{19}{2}x.

$$\frac{19}{2}x-1=37+r$$

Add 1 to both sides.

$$\frac{19}{2}x=37+r+1$$

Add 37 and 1 to get 38.

$$\frac{19}{2}x=38+r$$

The equation is in standard form.

$$\frac{19}{2}x=r+38$$

Divide both sides of the equation by \frac{19}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{19}{2}x}{\frac{19}{2}}=\frac{r+38}{\frac{19}{2}}$$

Dividing by \frac{19}{2} undoes the multiplication by \frac{19}{2}.

$$x=\frac{r+38}{\frac{19}{2}}$$

Divide 38+r by \frac{19}{2} by multiplying 38+r by the reciprocal of \frac{19}{2}.

$$x=\frac{2r}{19}+4$$