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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

4. Solving Equations With Variables on Both Sides

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Exercise 25 Page 106

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side. Start by using the Distributive Property.

r=18

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. In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

2r-(5-r)=13+2r

Distribute -1

2r-5-(- r)=13+2r

a-(- b)=a+b

2r-5+r=13+2r

Add terms

3r-5=13+2r

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

3r-5=13+2r

LHS-2r=RHS-2r

3r-5-2r=13+2r-2r

Subtract terms

r-5=13

LHS+5=RHS+5

r-5+5=13+5

Add terms

r=18

The solution to the equation is r=18. We can check our work by substituting it back into the original equation.

2r-(5-r)=13+2r

r= 18

2( 18)-(5- 18) ? = 13+2( 18)

Multiply

36-(5-18) ? = 13+36

Subtract term

36-(-13) ? = 13+36

a-(- b)=a+b

36+13 ? = 13+36

Add terms

49=49 ✓

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

Subchapter links

Lesson Check p.105

Practice and Problem-Solving Exercises p.105-108

Standardized Test Prep p.108

Mixed Review p.108