Exercise 19 Page 276

To solve the equation, we have to isolate a on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by 3. This will eliminate the denominator of the fraction.

5/7a=25

MoveRightFacToNum

a/c* b = a* b/c

5* a/7=25

MultEqn

LHS * 7=RHS* 7

5* a/7* 7=25* 7

FracMultDenomToNumber

a/7* 7 = a

5 * a=25* 7

Multiply

5a=175

Now, we will apply the Division Property of Equality. We will divide both sides of the equation by 5. This will eliminate the multiplication and isolate a.

5a=175

DivEqn

.LHS /5.=.RHS /5.

5a/5=175/5

CancelCommonFac

Cancel out common factors

5a/5=175/5

SimpQuot

Simplify quotient

a=175/5

CalcQuot

Calculate quotient

a=35

To check that this solution is correct, let's substitute a=35 into the original equation and simplify.

5/7a=25

Substitute

a= 35

5/7 * 35? =25

MoveRightFacToNum

a/c* b = a* b/c

5* 35/7? =25

Multiply

175/7? =25

CalcQuot

Calculate quotient

25=25 ✓

Since the left-hand side and right-hand side are equal, a=35 is the correct solution.

Extra

Properties of Equality

There are four main Properties of Equality that we use when solving linear equations.

Properties of Equality
Addition Property of Equality	If a=b, then a+c=b+c.
Subtraction Property of Equality	If a=b, then a-c=b-c.
Multiplication Property of Equality	If a=b, then ac=bc.
Division Property of Equality	If a=b and c is not 0, then a/c=b/c.

In later chapters, you will learn about some more advanced Properties of Equality. As an example, there is a property for when we need to eliminate a radical or an exponent.

Power Property of Equality
If a=b, then a^m=b^m.

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