Students compute a grand total for goody bags and are told to ensure the total sum is less than the $50 parents offered; the planning and Spending Your Money activities ask students to verify the final cost is under the $50 budget. The Spending Your Money questions explicitly ask whether the total (after tax) is over or under the $50 budget and to calculate by how much. The example solution shows comparing the total to $50 (e.g., $50.00 − $45.41 = $4.59, under budget).

Students practice using the symbols > and < to compare numbers and write inequalities (Activity 4 asks students to write inequalities comparing -3 and -9, compare 3 and |−5|, and to express recipe and temperature comparisons as inequalities). Students also write inequalities in real-world contexts (e.g., Benny's score 16 > −12, temperatures in Chillville wri<ten as (−)25 < (−)16, and a balloon vs. submersible d<stance compared with |325| < |−1052|). Students plot and label individual numbers on number lines to support their comparisons (several activities require plotting points such as −3 1/2 and −4).

Students complete problems that require using the symbols > and < (e.g., fill in each blank with >, <, or =). The unit description and parent plan explicitly list "Solve inequalities that involve positive and negative numbers and absolute value" and "Understand and solve problems involving inequalities" as skills to be addressed. Some practice items involve comparing values and absolute values (for example, items that ask students to complete >, <, = statements involving negatives and absolute value).

Students write inequalities from real-world contexts such as Casper's neighbor (n > 11) and José paying more than $5 (x > 5). Students are instructed to write inequalities from number-line graphs and complete activities that match word constraints to inequalities (e.g., 'n is greater than seven' → n > 7). The lesson explicitly discusses that inequalities like x &#<003e; c or x < c have infinitely many solutions (ellipses, solution-set notation) and shows how to represent those solutions on number lines with open/closed dots and arrows.

Students are asked to write inequalities from real-world word problems using a variable (e.g., Mateo: n + 4 < 10, Ellie: n - 4 > 2) and the Parent Plan explicitly lists "Write an inequality of the form x > c or x < c" as a skill. Multiple student activity pages require students to solve inequalities and graph their solution sets on number line diagrams. The lesson text explicitly states that inequalities like these have infinitely many solutions and shows solution sets with ellipses and number-line graphs, and students are instructed to check solutions by substitution.

The lesson explicitly contrasts how one-variable equations and inequalities are graphed on a number line and shows an example image of 4x + 3 < 11 with the solution x < 2 indicated by an open circle and an arrow. Student activity pages include one-variable inequality problems (for example, p + 7 > 5 and 2a + 4 ≤ 4) where students solve for the variable and graph the solution on provided number lines. The answer key describes the inequality solutions (p > -2, a ≤ 0) and indicates open/closed dots with arrows to show the infinite solution sets.

Students are asked to write and solve inequalities in real-world contexts (e.g., Bryan: n - 3 < 6 → n < 9; Rich: n + 3 ≤ 12 → n ≤ 9; Naomi: 2n + 20 > 240 → n > 110; Leah: n/4 ≥ 25 → n ≥ 100). Multiple Student Activity Pages require students to graph solution sets on number lines and the Answer Key shows graphs with open/closed dots and arrows extending (e.g., n > -2, n ≠ 2, n ≤ 3). The Parent Plan Skills list explicitly includes "Write an inequality of the form x >< c or x < c" and "Recognize that inequalities of the form x > c or x < c have infinitely many solutions," directing students to represent solutions on number line diagrams.

The Parent Plan skills list explicitly states: "Write an inequality of the form x > c or x < c to represent a constraint or condition" and "Represent solutions of inequalities on number line diagrams." Student tasks require creating 4–6 inequalities using "more than/less than/at least/no more than" language and at least one inequality must have its solution plotted on a number line. Sample problems and images show inequalities (e.g., 2n - 6 > <, y/5 < 3) and a number line with an arrow indicating values greater than 5.

The Basic Skills Review #11 includes an inequality problem: students are asked to solve 4y - 7 < 5 and graph the solution on a provided number line. The answer key shows the solved form y < 3 and describes the graph as an open dot at 3 with an arrow extending left, indicating the number-line representation. The student activity page explicitly provides space for graphing the solution on a number line.

The lesson repeatedly states and uses the triangle inequality a + b > c (e.g., "The sum of the lengths of the two shorter sides of a triangle is always greater than the length of the longest side" and "a + b > c"). Students are asked to apply this inequality to select possible third-side lengths (for example, circling valid lengths given two side measures and the longest side). Several problems and answer keys require students to use the a + b > c relationship to decide which numeric lengths could form a triangle.

Students are asked to write and solve an inequality in the Basic Skills Review problem about Mickey's trophies: they set up n + 4 ≥ 12 and solve to find n ≥ 8 and identify the least number of trophies. The activity requires students to translate a real-world constraint into an algebraic inequality and manipulate the inequality to isolate the variable. The answer key shows the full setup and solution steps for this inequality.

The Basic Skills Review (Problem 3) asks students to graph the inequality y < 2 on a number line. The answer key includes an image showing an open circle at 2 with shading to the left, indicating students represent the solution set on a number line. This requires students to interpret and graph an inequality of the form variable < constant.

The Basic Skills Review includes Problem 7 asking students to solve the inequality n + 3 < 5 and graph the solution on a number line. The answer key gives a solution and describes a number-line graph with an open dot and an arrow, which has students practice producing an inequality in the form n < c and representing its solution on a number line.

The Basic Skills Review #16 includes a problem that asks students to model a constraint with an inequality: "Josie had 4 fish and then she bought some more fish. She now has no more than 9 fish. How many fish could Josie have bought? Solve using an inequality." The answer key shows the work 4 + n ≤ 9 and the solution n ≤ 5, so students write and solve an inequality that represents a real-world constraint.

The Parent Plan skills list explicitly includes "Write an inequality of the form x > c or x < c" and "Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams." In Activity 2, students solve the inequality n + 2 > 5, write the solution n > 3, and a number line is provided; the answer key shows an open dot at 3 with an arrow extending to the right. The activity also has students write and solve a real-world inequality (4 + n ≤ 10) and provides solution boxes and a number line for graphing.

Students repeatedly write inequalities that bound irrational values, for example 5 < <1a;30 < 6<and 4 < √20 < 5 when identifying closest perfect squares. While refining decimal approximations they record single-sided inequalities such as <1a;30 > 5.4 and √30 < 5.5. Students place these square-root values on number lines (with arrows at both ends) to show their approximate locations relative to integers.

Students set the cost equations equal (0.15x + 31.50 = 0.20x + 20.75) and solve for x = 215, then interpret the result by stating that "driving becomes cheaper than the train when the distance is greater than 215 miles." Students graph cost versus distance and compare regions of the graph to determine which option is cheaper above or below the intersection. Students use comparative language (e.g., "greater than 215 miles") to describe the condition under which one option is preferable.

Students determine break-even points and then state which option is better for quantities less than or greater than that point (e.g., the apple example: "If you needed 6 or fewer, buy individually; if you need 7 or more, buy the bag"). The streaming example has students conclude, in words, "If you watch fewer than 5 movies, choose StreamMore. If you watch more than 5 movies, choose CinemaNow." Activity directions repeatedly ask students to decide which option is cheaper for values less than or greater than the break-even x-value.

Students determine the number of solutions for algebraic sentences (e.g., problems 30 and 31) and label cases as "Infinite solutions" or "No solution." Students solve linear equations for x in several problems (23–27, 28–29) which gives practice with solution sets of linear relationships. The answer key explicitly identifies an equation as having "Infinite solutions," showing students encounter the concept of infinitely many solutions.