[scheduled:: 2025-01-06]

Equations and Inequalities

Links and useful resources

• IXL Grade 7 index
• IXL Grade 8 index
• AoPS Alcumus
• AoPS Prealgebra Outline with assignments
• Handwritten math converter
• IXL prealgebra practice index
• OpenSTAX Prealgebra-1 textbook

Lesson-specific resource links

• IXL add/sub mixed numbers
• IXL mul/div mixed numbers

Concept summary and connections

• solving inequalities
• simplfiying equations
• mixed-number arithmetic
• algebra with inequalities

Worked examples

• Inequalities work like equations, with a small but important difference
• Multiplying both sides by a negative number switches the direction of the inequality
  • The size of the number doesn't change, but the one that was more positive is now more negative, or vice versa
  • Adding, subtracting, and multiplying by positive numbers keeps the inequality unchanged
  • Raising both sides to a power can be tricky, pay close attention to the signs! $-\frac{1}{2}<\frac{1}{4}$ but ${(-\frac{1}{2})}^2=\frac{1}{4}>{\left(\frac{1}{4}\right)}^2=\frac{1}{16}$

Media resources

• Youtube search for "solving inequalities": https://www.youtube.com/results?search_query=solving inequalities
• Youtube search for "simplfiying equations": https://www.youtube.com/results?search_query=simplfiying equations

Guided practice

• $4\frac{2}{3}+7\frac{3}{7}$
• $3\frac{7}{8}÷2\frac{1}{5}$
• $9\frac{2}{7}\times 2\frac{3}{5}$

Homework

• #hw (math) sign in to AoPS Alcumus and explore it. 2025-01-07

Quiz stuff

• #quiz Evaluate $3\frac{1}{2}\cdot 4\frac{3}{5}$
• #quiz Simplify $\frac{x+7}{12}-\frac{2x-3}{6}$
• #quiz Simplify $(a+b)(a-b+4)$