The solution of the equation 13+frac{w}{7}=-18 is boxed{w=-217}.

Further explanation:

Given:

The equation is 13+frac{w}{7}=-18.

Calculation:

Method (1)

The given equation is as follows:

boxed{13+dfrac{w}{7}=-18}  

The above equation is a linear equation that has one degree.

The equation with one variable can be solved by moving all terms in to the one side and simplify the equation for the value of variable.

Subtract 13 on both sides in the equation (1) to obtain the value of w as follows,

begin{aligned}13+dfrac{w}{7}-13&=-18-13\13-13+dfrac{w}{7}&=-31\ dfrac{w}{7}&=-31end{aligned}  

Now, multiply 7 on both sides of the above equation as,

begin{aligned}7times dfrac{w}{7}&=-31times7\w&=-217end{aligned}

Therefore, the value of w is -217.

Method (2)

To obtain the solution of the equation (1), take least common multiple of the denominator of the left hand side of the equation as,

begin{aligned}13+dfrac{w}{7}&=-18\ dfrac{(13times7)+w}{7}&=-18\ dfrac{91+w}{7}&=-18end{aligned}  

Now, multiply by 7 on both sides of the above equation to obtain the value of w as follows,

begin{aligned}7timesleft(dfrac{91+w}{7}right)&=7times(-18)\91+w&=-126end{aligned}

Subtract 91 on both sides of the above equation as follows,

begin{aligned}91+w-91&=-126-91\w&=-217end{aligned}

Therefore, the value of w is -217.

Thus,  the solution of the equation 13+dfrac{w}{7}=-18 is boxed{w=-217}.

Learn more:

1. Learn more about equations brainly.com/question/1473992

2. A problem on line brainly.com/question/1575090

3. A problem on function brainly.com/question/1435353

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear equations

Keywords: Equation, 13+(w/7)=-18, variables, subtract, linear equations, one degree, multiply least common multiple, linear equation, mathematics.