2.3 Solving Equations and Inequalities

• What is an equation in mathematics?

  A mathematical statement
• What is a linear equation?

  Variable raised to power 1
• The properties of equality allow us to manipulate equations


  True
• What is the goal of solving an equation?

  Find the value of the variable
• What is the main goal when solving a linear equation?

  Isolate the variable
• Steps for solving a linear equation using the addition/subtraction method:

  1️⃣ Use the addition or subtraction property to get the variable term on one side

  2️⃣ Simplify the equation to isolate the variable
• Steps for solving a linear equation:

  1️⃣ Isolate the variable term on one side using addition or subtraction

  2️⃣ Simplify the equation

  3️⃣ Make the coefficient of the variable equal to 1 using multiplication or division

  4️⃣ Ensure the variable is alone on one side
• What is an inequality in mathematics?

  A relationship between unequal expressions
• When solving inequalities, the inequality symbol must be maintained throughout the process.


  True
• What does it mean to solve an equation?

  Find the value of the variable
• The properties of equality allow us to manipulate equations to solve for the unknown variable
• What condition must apply to 'c' in the division property of equality?

  c ≠ 0
• To solve a linear equation, the goal is to isolate the variable
• What does the inequality symbol '<' indicate?

  Less than
• When multiplying or dividing an inequality by a negative number, the inequality sign must be reversed
• Steps to solve a simple inequality

  1️⃣ Simplify the inequality

  2️⃣ Isolate the variable

  3️⃣ Solve for the variable
• All values of `x` less than 3 satisfy the inequality `2x + 3 < 9`.


  True
• The solution to `-2x < 4` is `x > -2`.

  True
• The equation `2x + 5 = 11` is a linear equation.


  True
• Steps to solve a linear equation using addition/subtraction

  1️⃣ Use addition or subtraction to get the variable term on one side

  2️⃣ Simplify the equation to isolate the variable
• The multiplication or division property is used to get the coefficient of the variable equal to 1
• What property is used to move the variable term to one side in the addition/subtraction method?

  Addition or subtraction
• When using the multiplication/division property, the coefficient of the variable must become equal to 1
• The solution to `2x + 5 = 11` is x = 3.

  True
• A variable in an equation represents an unknown quantity

  True
• A quadratic equation involves a variable raised to the power of 2
• Match the property of equality with its definition:

  Addition ↔️ If `a = b`, then `a + c = b + c`

  Subtraction ↔️ If `a = b`, then `a - c = b - c`

  Multiplication ↔️ If `a = b`, then `a * c = b * c`

  Division ↔️ If `a = b` and `c ≠ 0`, then `a / c = b / c`
• A quadratic equation involves a variable raised to the power of 2
• Steps for solving a linear equation using addition/subtraction:

  1️⃣ Use addition or subtraction property to get variable term on one side

  2️⃣ Simplify the equation to isolate the variable
• Steps for solving a linear equation using the multiplication/division method:

  1️⃣ Use the multiplication or division property to get the coefficient of the variable equal to 1

  2️⃣ Simplify the equation to isolate the variable
• Solving multi-step linear equations begins with simplifying the equation by distributing and combining like terms.


  True
• The inequality symbol `<` represents "less than."
• What is a variable in an equation?

  A symbol for an unknown quantity
• The properties of equality allow us to manipulate equations while maintaining their balance.

  True
• If a = b, then a + c = b + c

  True
• Simplifying an equation is a step in solving it using addition or subtraction


  True
• Combining like terms is part of simplifying multi-step linear equations


  True
• Match the inequality symbol with its definition:

  > ↔️ Greater than

  ≤ ↔️ Less than or equal to

  ≥ ↔️ Greater than or equal to
• Steps to solve the inequality 2x + 3 < 9

  1️⃣ Subtract 3 from both sides

  2️⃣ Simplify to 2x < 6

  3️⃣ Divide both sides by 2

  4️⃣ Simplify to x < 3
• If `a < b` and `c > 0`, then `a * c < b * c` is true.

  True