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Big Ideas Math: Modeling Real Life, Grade 7
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Big Ideas Math: Modeling Real Life, Grade 7 View details
3. Solving Two-Step Equations
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Exercise 26 Page 143

Start by adding 13 to both sides.

g=- 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 adding 13 to both sides.

3/5g-1/3=- 10/3
AddEqn

LHS+1/3=RHS+1/3

3/5g-1/3+1/3=- 10/3+1/3
â–¼
Add terms
AddNeg

a+(- b)=a-b

3/5g+(- 1/3)+1/3=- 10/3+1/3
MoveNegFracToNum

Put minus sign in numerator

3/5g+- 1/3+1/3= - 10/3+1/3
AddFrac

Add fractions

3/5g+- 1+1/3= - 10+1/3
AddTerms

Add terms

3/5g+0/3= - 9/3

0/a=0

3/5g+0= - 9/3
IdPropAdd

Identity Property of Addition

3/5g= - 9/3
MoveNegNumToFrac

Put minus sign in front of fraction

3/5g=- 9/3
CalcQuot

Calculate quotient

3/5g=- 3
Now, we are going to multiply the equation by 5, and then divide it by 3 using the Multiplication and Division Properties of Equality. This will help us get rid of the fraction. Let's go!

3/5g=- 3
MoveRightFacToNum

a/c* b = a* b/c

3g/5=- 3
MultEqn

LHS * 5=RHS* 5

3g/5 * 5= - 3 * 5
FracMultDenomToNumber

a/5* 5 = a

3g=- 3 * 5
Multiply

Multiply

3g = - 15
DivEqn

.LHS /3.=.RHS /3.

3g/3 = - 15/3
â–¼
Calculate quotient
MoveNegNumToFrac

Put minus sign in front of fraction

3g/3 =- 15/3
CalcQuot

Calculate quotient

g = - 5

The solution to the equation is g = - 5. We can check our solution by substituting it into the original equation.

3/5g-1/3=- 10/3
Substitute

g= - 5

3/5( - 5)-1/3 ? = - 10/3
â–¼
Simplify
MultPosNeg

a(- b)=- a * b

- 3/5* 5 -1/3 ? =- 10/3
FracMultDenomToNumber

a/5* 5 = a

- 3 -1/3 ? =- 10/3
Rewrite

Rewrite 3 as 9/3

- 9/3 -1/3 ? =- 10/3
MoveNegFracToNum

Put minus sign in numerator

- 9/3 -1/3 ? =- 10/3
SubFrac

Subtract fractions

- 9-1/3 ? =- 10/3
SubTerm

Subtract term

-10/3 ? =- 10/3
MoveNegNumToFrac

Put minus sign in front of fraction

- 10/3=- 10/3

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

Subchapter links expand_more
arrow_right Try It p.140-141
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Try It 2 (Page 140)
Try It 3 (Page 140)
Try It 4 (Page 140)
Try It 5 (Page 140)
Try It 6 (Page 140)
Try It 7 (Page 141)
Try It 8 (Page 141)
Try It 9 (Page 141)
arrow_right Self-Assessment for Concept & Skills p.141
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Self-Assessment for Concept & Skills 11 (Page 141)
Self-Assessment for Concept & Skills 12 (Page 141)
Self-Assessment for Concept & Skills 13 (Page 141)
Self-Assessment for Concept & Skills 14 (Page 141)
Self-Assessment for Concept & Skills 15 (Page 141)
Self-Assessment for Concept & Skills 16 (Page 141)
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arrow_right Self-Assessment for Problem Solving p.142
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arrow_right Review & Refresh p.143
Review & Refresh 1 (Page 143)
Review & Refresh 2 (Page 143)
Review & Refresh 3 (Page 143)
Review & Refresh 4 (Page 143)
Review & Refresh 5 (Page 143)
Review & Refresh 6 (Page 143)
Review & Refresh 7 (Page 143)
Review & Refresh 8 (Page 143)
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arrow_right Concept, Skills, & Problem Solving p.143-144
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Concept, Skills, & Problem Solving 11 (Page 143)
Concept, Skills, & Problem Solving 12 (Page 143)
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Concept, Skills, & Problem Solving 33 (Page 144)
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