Modeling Two-Step Equations and Inequalities

What is the equation for this model ?

• 3x + 4 = 13

• 3x - 4 = -1

• 6x = 14

• -3x + 4 = 13

If −𝟐(𝟓.𝟓𝒙 − 𝟔.𝟑) is equivalent to 𝒎𝒙 + 𝟏𝟐.𝟔, what is the value of 𝒎?

• 11

• 3.5

• -3.5

• -11

A tourist wants to spend at most $𝟑, 𝟓𝟎𝟎 on a cross-country adventure. The tourist has already spent $𝟕𝟓.

If the tourist has 10 weeks left in the trip, which inequality and graph represent the maximum amount of money 𝒎 the tourist can spend per week to stay within budget?

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A teacher asks a student to write and solve an inequality to find what numbers satisfy the statement that 3.2 more than 7 times a number, 𝒏, is less than 17.2. The table shows the student’s work. Which statement is true?

• The student’s work in all of the steps is correct because all numbers less than 7 satisfy the

  statement.

• The student made a mistake writing the inequality before Step 1. The correct inequality that

  represents the statement is 3.2𝑛 + 7 < 17.2.

• The student made a mistake between Step 1 and Step 2 by subtracting 3.2 from both sides of

  the inequality instead of adding 3.2 to both sides of the inequality.

• The student made a mistake between Step 2 and Step 3 by subtracting 7 from the right side

  of the inequality instead of dividing both sides of the inequality by 7.

The inequality 𝟐𝒄 − 𝟑 < 𝟗 represents the amount of money a student can spend on 𝒄 candy bars. Which statement is true?

• The solution to the inequality is 𝑐 < 3, and it represents that the student can buy a maximum of 3 whole candy bars.

• The solution to the inequality is 𝑐 < 3, and it represents that the student can buy a maximum of 2 whole candy bars.

• The solution to the inequality is 𝑐 < 6, and it represents that the student can buy a maximum of 6 whole candy bars.

• The solution to the inequality is 𝑐 < 6, and it represents that the student can buy a maximum of 5 whole candy bars.

A senior class saves money for the school prom. The class currently has $𝟒𝟎𝟎 saved and wants a total of $𝟕, 𝟔𝟎𝟎 for the prom. The class saves $𝟖𝟎 each day, 𝒅, to reach its goal. Which statement is true?

• The equation 80𝑑 + 400 = 7,600 can be used to find that it will take 90 days for the class to

  reach its goal at the current savings rate.

• he equation 80𝑑 + 400 = 7,600 can be used to find that it will take 100 days for the class to reach its goal at the current savings rate.

• The equation 80(𝑑 + 400) = 7,600 can be used to find that it will take 90 days for the class to reach its goal at the current savings rate.

• The equation 80(𝑑 + 400) = 7,600 can be used to find that it will take 100 days for the class to reach its goal at the current savings rate.

Which graph matches the inequality
k < 3?

• A

• B

• C

• D

Write an expression. 
Anita needs at least an 90 grade (g) on her test to get an A in math class.

• g ≤ 90

• g ≥ 90

• g < 90

• g > 90

126 < f + 32

• f > 94

• f < 96

• f < 94

• f < 55

The goal of solving a one, two, or multi-step equations is to:

• Find the constant

• Find the coefficient

• Find the value of the variable

• Guess and check