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Big Ideas Math: Modeling Real Life, Grade 7

BI

Big Ideas Math: Modeling Real Life, Grade 7 View details

3. Solving Two-Step Equations

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Exercise 6 Page 140

Start by subtracting 25 from both sides.

a=- 2/5

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, the only variable term is already on the left-hand side of the equation, so we will start by subtracting 25 from both sides.

2/5+4a=- 6/5

LHS-2/5=RHS-2/5

2/5+4a-2/5=- 6/5-2/5

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Simplify left-hand side

CommutativePropAdd

Commutative Property of Addition

4a+2/5-2/5=- 6/5-2/5

Subtract fractions

4a+2-2/5=- 6/5-2/5

Subtract term

4a+0/5=- 6/5-2/5

0/a=0

4a+0=- 6/5-2/5

Identity Property of Addition

4a=- 6/5-2/5

▼

Subtract fractions

MoveNegFracToNum

Put minus sign in numerator

4a= - 6/5-2/5

Subtract fractions

4a= - 6-2/5

Subtract term

4a= - 8/5

.LHS /4.=.RHS /4.

4a/4= - 85/4

Calculate quotient

a= - 85/4

▼

Simplify right-hand side

a/c/b= a/b* c

a = - 8/4* 5

Multiply

a = - 8/20

a/b=.a /4./.b /4.

a = - 8/4/20/4

Calculate quotient

x=- 2/5

MoveNegNumToFrac

Put minus sign in front of fraction

x=- 2/5

The solution to the equation is x=- 25. We can check our solution by substituting it into the original equation.

2/5+4a=- 6/5

x= - 2/5

2/5+4( - 2/5 ) ? = - 6/5

▼

Simplify

MoveNegFracToNum

Put minus sign in numerator

2/5+4( - 2/5 ) ? = - 6/5

MoveLeftFacToNum

a*b/c= a* b/c

2/5+ 4 (- 2)/5 ? = - 6/5

a(- b)=- a * b

2/5+ - 4* 2/5 ? = - 6/5

Multiply

2/5+ - 8/5 ? = - 6/5

Add fractions

2+( - 8)/5 ? = - 6/5

Add terms

- 6/5 ? = - 6/5

MoveNegNumToFrac

Put minus sign in front of fraction

- 6/5= - 6/5

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

Subchapter links

Try It p.140-141

Self-Assessment for Concept & Skills p.141

Self-Assessment for Problem Solving p.142

Review & Refresh p.143

Concept, Skills, & Problem Solving p.143-144