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Big Ideas Math: Modeling Real Life, Grade 8
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Big Ideas Math: Modeling Real Life, Grade 8 View details
7. Writing Equations in Point-Slope Form
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Exercise 4 Page 183

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

x=8/9

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.

6x-7=1-3x
AddEqn

LHS+3x=RHS+3x

6x-7+3x=1-3x+3x
CommutativePropAdd

Commutative Property of Addition

6x+3x-7=1+3x-3x
AddSubTerms

Add and subtract terms

9x-7=1
Now, we can continue to solve using the Properties of Equality.

9x-7=1
AddEqn

LHS+7=RHS+7

9x-7+7=1+7
AddTerms

Add terms

9x=8
DivEqn

.LHS /9.=.RHS /9.

9x/9=8/9
MovePartNumRight

a* b/c=a/c* b

9/9 * x=8/9
CalcQuot

Calculate quotient

1 * x=8/9
IdPropMult

Identity Property of Multiplication

x=8/9

The solution to the equation is x= 89. We can check our solution by substituting it into the original equation.

6x-7=1-3x
Substitute

x= 8/9

6( 8/9)-7 ? = 1-3( 8/9)
â–¼
Simplify
MoveLeftFacToNum

a*b/c= a* b/c

6 * 8/9-7 ? = 1-3 * 8/9
Multiply

Multiply

48/9-7 ? = 1-24/9
NumberToFrac

a = 9* a/9

48/9-7 * 9/9? = 1-24/9
Multiply

Multiply

48/9-63/9 ? = 1-24/9
OneToFrac

Rewrite 1 as 9/9

48/9-63/9 ? = 9/9-24/9
SubFrac

Subtract fractions

48-63/9 ? = 9-24/9
SubTerms

Subtract terms

-15/9 ? = -15/9
MoveNegNumToFrac

Put minus sign in front of fraction

-15/9 = -15/9 ✓

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.180-181
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Try It 2 (Page 180)
Try It 3 (Page 180)
Try It 4 (Page 181)
Try It 5 (Page 181)
arrow_right Self-Assessment for Concepts & Skills p.181
Self-Assessment for Concepts & Skills 6 (Page 181)
Self-Assessment for Concepts & Skills 7 (Page 181)
Self-Assessment for Concepts & Skills 8 (Page 181)
Self-Assessment for Concepts & Skills 9 (Page 181)
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arrow_right Self-Assessment for Problem Solving p.182
Self-Assessment for Problem Solving 11 (Page 182)
Self-Assessment for Problem Solving 12 (Page 182)
arrow_right Review & Refresh p.183
Review & Refresh 1 (Page 183)
Review & Refresh 2 (Page 183)
Review & Refresh 3 (Page 183)
Review & Refresh 4 (Page 183)
Review & Refresh 5 (Page 183)
arrow_right Concepts, Skills, & Problem Solving p.183-184
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Concepts, Skills, & Problem Solving 7 (Page 183)
Concepts, Skills, & Problem Solving 8 (Page 183)
Concepts, Skills, & Problem Solving 9 (Page 183)
Concepts, Skills, & Problem Solving 10 (Page 183)
Concepts, Skills, & Problem Solving 11 (Page 183)
Concepts, Skills, & Problem Solving 12 (Page 183)
Concepts, Skills, & Problem Solving 13 (Page 183)
Concepts, Skills, & Problem Solving 14 (Page 183)
Concepts, Skills, & Problem Solving 15 (Page 183)
Concepts, Skills, & Problem Solving 16 (Page 183)
Concepts, Skills, & Problem Solving 17 (Page 183)
Concepts, Skills, & Problem Solving 18 (Page 183)
Concepts, Skills, & Problem Solving 19 (Page 183)
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Concepts, Skills, & Problem Solving 27 (Page 184)
Concepts, Skills, & Problem Solving 28 (Page 184)
Concepts, Skills, & Problem Solving 29 (Page 184)
Concepts, Skills, & Problem Solving 30 (Page 184)