Exercise 11 Page 63

To solve the given literal equation for x, we will use the Properties of Equality to apply inverse operations on the equation. Remember, only like terms can be combined. Since the inverse operation to addition is subtraction, to eliminate 6 from the right-hand side we have to subtract 6 from both sides of the equation. Next, we have to factor out x.

y-6=4x+zx

FactorOut

Factor out x

y-6= x(4+z)

Now, we have to eliminate the parenthetical factor. To do it we have to divide both sides of the equation by 4+z.

y-6=x(4+z)

DivEqn

.LHS /(4+z).=.RHS /(4+z).

y-6/4+z= x(4+z)/4+z

CancelCommonFac

Cancel out common factors

y-6/4+z=x

Finally, to find our final answer, we will rearrange the equation and the terms in the denominator.

y-6/4+z=x

RearrangeEqn

Rearrange equation

x=y-6/4+z

CommutativePropAdd

Commutative Property of Addition

x=y-6/z+4