Algebra Chapter 1A Test Review

Writing Inequalities

• Translate word sentences into inequalities for mathematical expressions.
• Example: n - 4.1 > 15 translates to n > 19.1.
• Example: 3c + 16 ≥ 5 translates to 3c ≥ -11, then c ≥ -11/3.

Testing Solutions to Inequalities

• Determine if given values satisfy specific inequalities.
• For y + 4 ≤ 1 with y = -3, the solution is valid since -3 + 4 = 1.
• For x/5 > -4 with x = -18, the solution is invalid since -18/5 = -3.6 which is not greater than -4.

Solving and Graphing Inequalities

• Solve basic inequalities, ensuring to express solutions properly.
• Graph solutions on a number line.
• Example: y + 7 ≥ -2, solve as y ≥ -9; indicate all values greater than or equal to -9.
• Example: x - 2 ≤ 4, solve as x ≤ 6; indicate all values less than or equal to 6.

Key Inequality Problems

• 2r > 18 results in r > 9.
• r/7 ≤ 3 results in r ≤ 21.
• -4k > 24 results in k < -6.
• 6w - 7 ≤ -13 becomes 6w ≤ -6, leading to w ≤ -1.
• -6x - 6 ≥ -36 leads to -6x ≥ -30, so x ≤ 5.
• 3d + 2 > -10 results in d > -4.

Word Problems and Inequalities

• A small cruise ship with a capacity of 500 people and 115 crew members can take 385 additional passengers. The inequality is p ≤ 385.
• For fundraising, with a requirement of at least $50 and $15 already raised, the inequality 3.50c + 15 ≥ 50 leads to c ≥ 10, meaning 10 candles must be sold.
• In the rectangle problem with a base of 12 cm and height of (x - 7) cm, the inequality x - 7 > 12 leads to x > 19, indicating the height must be greater than 19 cm.

Prepare for your Algebra Chapter 1A test with this comprehensive review. You will practice writing word sentences as inequalities, determining solutions, and solving various inequalities while learning to graph your results. This quiz also includes real-world applications through word problems.