6th Grade Equations and Inequalities Unit 5 Test

Which calculation would need to be done to solve the equation 2x = 26?

What is the solution to the inequality x ≥ 23?

Which of these situations can be modeled by the inequality x < 250?

If the solution to an inequality is t ≤ 7, what does it mean?

Solve the equation x − 20.7 = 9.5 for x.

Which equation is true when n = 4?

Which of the following numbers make the inequality $m > 0$ true?

What is the solution to the equation $0.3r = 2.1$?

Which number is not part of the solution set to the inequality $w - 10 ≤ 16$?

What is the solution set for the inequality $6x ≥ 42$?

Which inequality is represented by the graph?

What are the dependent and independent variables in the graph?

Which equation can be used to determine the number of hours Joanna worked last week, if she earns $12 per hour and earned $432?

Joanna earns $12 per hour at her job. What is the number of hours Joanna worked last week if she earned $432?

A player purchased 4 jerseys for a total of $75.96. What is the cost, in dollars, of each jersey?

Equation and Inequality Solutions

To solve the equation 2x = 26, divide both sides by 2, resulting in x = 13.
The solution to the inequality x ≥ 23 means that x can be any number greater than or equal to 23.
The inequality x < 250 can model situations where a quantity is limited to below 250, such as budget constraints or maximum capacity.

Interpretation of Inequalities

An inequality t ≤ 7 indicates that t can be any value less than or equal to 7.
To solve the equation x − 20.7 = 9.5, add 20.7 to both sides to find x = 30.2.

Relationships and Variables

For n = 4, a true equation could be something like n + 2 = 6, which holds true when substituting n.
The values that satisfy the inequality m > 0 are any positive numbers (e.g., 1, 2, 3).

Solving Linear Equations

The solution to the equation 0.3r = 2.1 is found by dividing 2.1 by 0.3, resulting in r = 7.
The inequality w - 10 ≤ 16 does not include numbers greater than 26, making 27 not part of the solution set.

Graphs and Relations

The solution set for the inequality 6x ≥ 42 can be found by dividing both sides by 6, leading to x ≥ 7.
The graph represented by an inequality can be analyzed to determine boundaries, such as open (strict) or closed (inclusive) intervals.

Application of Equations

To determine hours worked when Joanna earns $12 per hour, the equation is 12h = 432 where h represents hours worked.
Solving 12h = 432 yields h = 36, indicating Joanna worked 36 hours last week.

Cost Calculation

If a player purchased 4 jerseys for $75.96, the cost per jersey is calculated by dividing the total cost by the number of jerseys, resulting in each jersey costing $18.99.

This quiz covers solving equations, understanding inequalities, and matching descriptions with the correct inequality. It includes questions on solving for unknown variables, identifying true equations, and matching scenarios with the appropriate inequality.