14.2.1 Applying algebraic manipulation

• Algebraic symbols are the letters and numbers used to represent unknown or variable values
• What is the value of `x` in the equation `3x + 5 = 14`?

  3
• Steps to solve `2 × (3 + 4)² ÷ 14 - 3`

  1️⃣ Evaluate parentheses: `3 + 4 = 7`

  2️⃣ Calculate exponent: `7² = 49`

  3️⃣ Multiply and divide: `2 × 49 = 98`, `98 ÷ 14 = 7`

  4️⃣ Subtract: `7 - 3 = 4`
• In solving linear equations, the variable must be isolated on one side of the equation.

  True
• Variables in algebraic symbols are often denoted by letters like `x`, `y`, or t
• In the multiplication `2x × 3y`, the result is 6xy
• Multiplication in algebra involves multiplying the coefficients
• The order of operations is often remembered using the acronyms PEMDAS or BODMAS.
• In the example `2 × 49 ÷ 14 - 3`, after division, the expression becomes 7 - 3
• Variables in algebraic expressions are often denoted by letters like `x`, `y`, or `t`.


  True
• Understanding algebraic notation is crucial for solving physics problems efficiently.

  True
• Addition in algebra combines two or more terms by adding their coefficients
• What is the simplified form of `3x + 2y - x + 4y`?

  2x + 6y
• What is the value of `x` in the equation `3x + 5 = 14`?

  3
• Variables are the letters and numbers used to represent unknown or variable values
• To solve the equation `3x + 5 = 14`, the first step is to subtract `5` from both sides
• In the operation `2x + 3x = 5x`, the coefficients are added to combine like terms
• Steps to perform fundamental algebraic operations

  1️⃣ Identify the variables and their coefficients

  2️⃣ Apply the appropriate operation to the coefficients

  3️⃣ Ensure the variable terms are correctly represented
• Parentheses should always be evaluated first in the order of operations.


  True
• Variables represent unknown quantities in algebraic expressions, while constants represent fixed numerical values
• Constants in algebraic expressions have fixed numerical values
• What is the result of `2x × 3y`?

  6xy
• Variables in algebra are often denoted by letters like `x`, `y`, or `t`.


  True
• Match the symbol type with its description:

  Variables ↔️ Represent unknown quantities

  Constants ↔️ Fixed numerical values

  Operators ↔️ Actions performed on variables

  Coefficients ↔️ Numbers multiplying variables
• Understanding algebraic notation is crucial for solving physics problems.


  True
• Steps to solve the equation `3x + 5 = 14`

  1️⃣ Subtract `5` from both sides: `3x = 9`

  2️⃣ Divide both sides by `3`: `x = 3`
• In multiplication, the coefficients of two terms are multiplied together.

  True
• To simplify `3x + 2y - x + 4y`, the first step is to group like terms
• In the expression `2 × (3 + 4)² ÷ 14 - 3`, the first step is to evaluate the parentheses
• What is the primary goal of solving a linear equation?

  Find the variable value
• Steps to solve the linear equation `5x - 7 = 18`

  1️⃣ Add `7` to both sides: `5x = 25`

  2️⃣ Divide both sides by `5`: `x = 5`
• Constants in algebraic symbols have fixed numerical values.

  True
• Steps to perform fundamental algebraic operations

  1️⃣ Identify the variables and their coefficients

  2️⃣ Apply the appropriate operation to the coefficients

  3️⃣ Ensure the variable terms are correctly represented
• Division in algebra divides the coefficient of one term by another.

  True
• Parentheses are always performed first in the order of operations.

  True
• What is the goal when solving a linear equation?

  Find the variable's value
• Factoring is the only method to solve quadratic equations.

  False
• What is the general form of a quadratic equation?

  $ax^{2} +$$bx +$$c =$$0$
• When using factoring to solve a quadratic equation, what do you need to find?

  Two numbers that multiply to ac and add to b
• What is the product rule for indices?

  $a^{m} × a^{n} =$$a^{m + n}$