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.