Exercise 18 Page 194

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the properties of equality. x/2+x/6=7 In this case, the variable terms are all already on the left-hand side of the equation, so we will start by eliminate the fractions. Since 6 is a common multiple of 2 and 6, we can multiply both sides of the equation by 6 to get rid the fractions of the equation.

x/2+x/6=7

MultEqn

LHS * 6=RHS* 6

6(x/2+x/6)=6* 7

Distr

Distribute 6

6* x/2+6 * x/6=6* 7

MoveLeftFacToNum

a*b/c= a* b/c

6* x/2+6* x/6=6* 7

Multiply

6x/2+6x/6=42

CalcQuot

Calculate quotient

3x+x=42

Now we can combine like terms and continue to solving the equation.

3x+x=42

AddTerms

Add terms

4x=42

DivEqn

.LHS /4.=.RHS /4.

4x/4=42/4

CalcQuot

Calculate quotient

x=10.5

The solution of the equation is x=10.5.

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the properties of equality. x/9+2x/2=1/3 In this case, the variable terms are all already on the left-hand side of the equation, so we will start by eliminate the fractions. Since 18 is a common multiple of 2 and 9, we can multiply both sides of the equation by 18 to get rid the fractions of the equation.

x/9+2x/2=1/3

MultEqn

LHS * 18=RHS* 18

18(x/9+2x/2)=18* 1/3

Distr

Distribute 18

18* x/9+18 * 2x/2=18* 1/3

MoveLeftFacToNum

a*b/c= a* b/c

18* x/9+18* 2x/2= 18* 1/3

Multiply

18x/9+36x/2=18/3