16z+116=-48

A mixed number is an addition of its whole and fractional parts.

16z+1+16=-48

Add 1 and 16.

Write 1 as a fraction with a common denominator.

16z+66+16=-48

Combine the numerators over the common denominator.

16z+6+16=-48

Add 6 and 1.

16z+76=-48

16z+76=-48

16z+76=-48

Subtract 76 from both sides of the equation.

16z=-48-76

To write -48 as a fraction with a common denominator, multiply by 66.

16z=-48⋅66-76

Combine -48 and 66.

16z=-48⋅66-76

Combine the numerators over the common denominator.

16z=-48⋅6-76

Simplify the numerator.

Multiply -48 by 6.

16z=-288-76

Subtract 7 from -288.

16z=-2956

16z=-2956

Move the negative in front of the fraction.

16z=-2956

16z=-2956

Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 6z. The -2956 expression needs to be multiplied by zz to make the denominator 6z.

16z=-2956⋅zz

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 6z.

295(z)

Multiply 295 by z.

16z=-295z6z

16z=-295z6z

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

1=-(295z)

Rewrite the equation as -(295z)=1.

-(295z)=1

Multiply 295 by -1.

-295z=1

Divide each term in -295z=1 by -295.

-295z-295=1-295

Cancel the common factor of -295.

Cancel the common factor.

-295z-295=1-295

Divide z by 1.

z=1-295

z=1-295

Move the negative in front of the fraction.

z=-1295

z=-1295

The result can be shown in multiple forms.

Exact Form:

z=-1295

Decimal Form:

z=-0.00338983…

Solve for z 1/(6z)+1 1/6=-48