Exercise 53 Page 552

To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side using the Properties of Equality. In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

2(x+3)+7=- 11

Distr

Distribute 2

2* x+2* 3+7=- 11

Multiply

Multiply

2x+6+7=- 11

AddTerms

Add terms

2x+13=- 11

Now, we can continue to solve using the Properties of Equality.

2x+13= -11

SubEqn

LHS-13=RHS-13

2x+13-13=- 11-13

SubTerm

Subtract term

2x=- 24

DivEqn

.LHS /2.=.RHS /2.

2/2x=- 24/2

CalcQuot

Calculate quotient

x=- 12

The solution to the equation is x=- 12, so the correct answer is F.