2 Pull It All Together

BIG idea Equivalence

You can represent an equation in many ways. Equivalent representations have the same solution as the original equation.

Task 1

The solution of the equation is shown. Use mathematical properties to explain your answers in each part below.

1. Explain why you can subtract from each side in Step 2.
2. Write another equation that is equivalent to . Justify your answer.

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BIG idea Solving Equations and Inequalities

You can use properties of numbers and equality to transform equations into equivalent, simpler equations and find solutions.

Task 2

Solve using two different methods. Explain which method you prefer to use.

1. 24 = 2 3 x + 12 24 equals , 2 thirds , x plus 12
2. 0.5 ( y + 12 ) = − 2.5 y − 8 0.5 open y plus 12 close equals negative 2.5 y minus 8
3. x − 3 5 = 3 x 7 fraction x minus 3 , over 5 end fraction . equals , fraction 3 x , over 7 end fraction

BIG idea Proportionality

In a proportional relationship, the ratios of two quantities are equal. You can use this relationship to describe similar figures, scale models, and rates.

Task 3

Solve. Show all your work and explain your steps.

A family rents a truck to move from Buffalo to Chicago. The rental has a base cost of $49.95, plus an additional cost of $1.19 per mile driven. The family also pays for gas, which costs $3.89 per gallon. The truck's average gas mileage is 18 miles per gallon. What is the total cost of the move? (Hint: Use the map to estimate the driving distance.)

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