Exercise 21 Page 153

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

14.7

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 using the Properties of Equality. In this case, we start by expanding the fraction to isolate x.

2x/7+4/5=5

a/b=a * 5/b * 5

2x*5/7*5+4/5=5

a/b=a * 7/b * 7

2x*5/7*5+4*7/5*7=5

10x/35+28/35=5

Add fractions

10x+28/35=5

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

10x+28/35=5

LHS * 35=RHS* 35

10x+28/35*35=5*35

a/35* 35 = a

10x+28=175

LHS-28=RHS-28

10x=147

.LHS /10.=.RHS /10.

x=14.7

The solution to the equation is x=14.7. We can check our solution by substituting it into the original equation.

2x/7+4/5=5

x= 14.7

2* 14.7/7+4/5? =5

29.4/7+4/5? =5

Calculate quotient

4.2+0.8? =5

Add terms

5=5

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

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