Exercise 41 Page 206

To solve an equation, we should 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. Now we can continue to solve using the Properties of Equality.

14n+77=4n

SubEqn

LHS-4n=RHS-4n

14n+77-4n=4n-4n

SubTerms

Subtract terms

10n+77=0

SubEqn

LHS-77=RHS-77

10n+77-77=0-77

SubTerms

Subtract terms

10n=- 77

DivEqn

.LHS /10.=.RHS /10.

10n/10 = -77/10

CalcQuot

Calculate quotient

n=-7.7

The solution to the equation is n=-7.7. We can check our solution by substituting it into the original equation.

7(2n+11)=4n

Substitute

n= -7.7

7(2( -7.7)+11) ? = 4( -7.7)

▼

Simplify

MultPosNeg

a(- b)=- a * b

7(-15.4+11) ? = -30.8

AddTerms

Add terms

7(-4.4) ? = -30.8

MultPosNeg

a(- b)=- a * b

-30.8=-30.8

Since the left-hand side is equal to the right-hand side, our solution is correct.