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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

2. Solving Two-Step Equations

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Exercise 42 Page 92

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

- 21/2

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side using the Properties of Equality. In this case, we need to eliminate the fraction by multiplying both sides by 3 in order to isolate the variable term.

x-3/3=- 4 12

LHS * 3=RHS* 3

3(x-3/3)=3(- 4 12)

a bc=a* c+b/c

3(x-3/3)=3(- 4* 2 + 1/2)

Multiply

3(x-3/3)=3(- 8 + 1/2)

Add terms

3(x-3/3)=3(- 9/2)

MoveLeftFacToNum

a*b/c= a* b/c

3(x-3)/3=- 3* 9/2

CancelCommonFac

Cancel out common factors

3(x-3)/3=- 3* 9/2

Simplify quotient

x-3=- 3* 9/2

LHS+3=RHS+3

x-3+3=- 3* 9/2+3

Add terms

x=- 3* 9/2+3

Now, we can simplify the right-hand side of the equation.

x=- 3* 9/2+3

▼

Evaluate

Multiply

x=- 27/2+3

a = 2* a/2

x=- 27/2+2(3)/2

Multiply

x=- 27/2+6/2

MoveNegFracToNum

Put minus sign in numerator

x=- 27/2+6/2

Add fractions

x=- 27+6/2

Add terms

x=- 21/2

The solution to the equation is x= - 212. We can check our solution by substituting it into the original equation.

x-3/3=- 4 12

x= - 21/2

- 212-3/3 ? = - 4 12

▼

Evaluate

a bc=a* c+b/c

- 212-3/3 ? = - 4* 2 + 1/2

a = 2* a/2

- 212- 2(3)2/3 ? = - 4* 2 + 1/2

Multiply

- 212- 62/3 ? = - 8 + 1/2

Add terms

- 212- 62/3 ? = - 9/2

MoveNegFracToNum

Put minus sign in numerator

- 212- 62/3 ? = - 9/2

Subtract fractions

- 21-62/3 ? = - 9/2

Subtract terms

- 272/3 ? = - 9/2

a/c/b= a/b* c

- 27/3(2) ? = - 9/2

a/b=a * 3/b * 3

- 27/3(2) ? = - 9(3)/2(3)

Multiply

- 27/6 = - 27/6

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

Subchapter links

Lesson Check p.91

Practice and Problem-Solving Exercises p.91-93

Standardized Test Prep p.93

Mixed Review p.93