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Big Ideas Math Geometry, 2014 View details

4. Algebraic Reasoning

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Exercise 1 Page 92

Use inverse operations until you have fully isolated x.

Solution: x=-4
Justifications:

Operation	Simplify	Reason	Property used
6x-11 + 11=-35 + 11	6x=-24	To eliminate the constant term from the left-hand side.	Addition Property of Equality
6x/6=-24/6	x=-4	To eliminate the coefficient.	Division Property of Equality

Practice makes perfect

To solve the equation, we have to isolate x on one side using inverse operations. To begin, we want to collect all of the constants on one side of the equation. The inverse operation of subtraction is addition, so to eliminate - 11 we have to add 11 to both sides of the equation.

6x-11=-35

AddEqn

LHS+11=RHS+11

6x-11 + 11 =- 35 + 11

AddTerms

Add terms

6x=-24

Then, we have to eliminate the coefficient 6. Since multiplication and division are inverse operations, we have to divide by 6.

6x=-24

DivEqn

.LHS /6.=.RHS /6.

6x/6=-24/6

CalcQuot

Calculate quotient

x=- 4

The solution to the equation is x=-4. Let's name the property we used in each step.

Operation	Simplify	Reason	Property used
6x-11 + 11=-35 + 11	6x=-24	To eliminate the constant term from the left-hand side.	Addition Property of Equality
6x/6=-24/6	x=-4	To eliminate the coefficient.	Division Property of Equality

Subchapter links

Communicate Your Answer p.91

Monitoring Progress p.92-95

Exercises p.96-98

Exercise 1 Page 92

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