Exercise 28 Page 9

To solve the equation, we have to isolate x on one side. Using the Division Property of Equality, we will divide both sides of the equation by - 7.8. This will eliminate the coefficient of x and isolate it on the left-hand side of the equation.

- 7.8x=- 1.56

DivEqn

.LHS /(- 7.8).=.RHS /(- 7.8).

- 7.8x/- 7.8=- 1.56/- 7.8

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Simplify left-hand side

ReduceFrac

a/b=.a /(- 7.8)./.b /(- 7.8).

x/1=- 1.56/- 7.8

DivByOne

a/1=a

x=- 1.56/- 7.8

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Simplify right-hand side

FactorOut

Factor out (- 1.56)

x=- 1.56/- 1.56(5)

ReduceFrac

a/b=.a /(- 1.56)./.b /(- 1.56).

x=1/5

WriteDec

Write as a decimal

x=0.2

To check that this solution is correct, let's substitute x= 0.2 into the original equation and simplify.

- 7.8x=- 1.56

Substitute

x= 0.2

- 7.8( 0.2)? =- 1.56

Multiply

Multiply

- 1.56=- 1.56 ✓

Since the left-hand side and right-hand side are equal, x=0.2 is the correct solution.