14.2.1 Applying algebraic manipulation

• What is a variable in algebra?

  Symbol for unknown quantity
• Give an example of a variable in the expression 3x + 5</latex>.

  $x$
• An expression is a combination of variables, constants, and operators
• What is an equation in algebra?

  Two expressions set equal
• Give an example of an equation in algebra.

  $2z +$$1 =$$9$
• What operation is performed first to solve 2x + 3 = 7</latex> for $x$?


  Subtract 3
• What mathematical operations are used to move terms and isolate variables in algebraic equations?

  Addition, subtraction, multiplication, division
• An equation is formed by setting two expressions equal to each other.


  True
• What is the final value of $x$ when solving the equation $2x +$$3 =$$7$?


  $x =$$2$
• An expression combines variables, constants, and operators
• Steps to solve the equation 2x + 3 = 7</latex>

  1️⃣ Subtract 3 from both sides

  2️⃣ Divide both sides by 2
• An expression combines variables, constants, and operators like addition or multiplication.


  True
• How do you isolate $x$ when solving 2x + 3 = 7</latex>?


  Subtract 3 and divide by 2
• Match the algebraic concept with its example:

  Variable ↔️ $x$, $y$, $z$

  Expression ↔️ $3x +$$2$, $4y - 5$

  Equation ↔️ $2x +$$3 =$$7$, $5y - 1 =$$14$
• To isolate a variable, you can use operations like addition, subtraction, multiplication, and division
• Steps to solve the equation 2x + 3 = 7</latex>

  1️⃣ Subtract 3 from both sides

  2️⃣ Divide both sides by 2
• Algebraic manipulation involves moving terms and isolating the variable
• An equation sets two expressions equal to each other.


  True
• To solve algebraic equations, you must isolate the variable
• Match the algebraic concept with its description:

  Variable ↔️ Symbol representing an unknown quantity

  Expression ↔️ Combination of variables, constants, and operators

  Equation ↔️ Two expressions set equal to each other
• The solution to the equation 2x + 3 = 7</latex> is $x =$$2$.


  True
• In the substitution method, you solve one equation for a variable and substitute it into the other equation
• Cross-multiplication is used for equations in the form $\frac{a}{b} =$$\frac{c}{d}$, where you multiply $ad =$$bc$ and solve for the desired variable
• In elimination, after adding or subtracting equations, you solve for the remaining variable
• Match the algebraic concept with its example:

  Variable ↔️ $x$, $y$, $z$

  Expression ↔️ $3x +$$2$, $4y - 5$

  Equation ↔️ $2x +$$3 =$$7$, $5y - 1 =$$14$
• A variable is usually represented by a letter
• What is an expression in algebra?

  Combination of variables, constants, and operators
• Give an example of an expression in algebra.

  $4y - 7$
• An equation always involves the equality symbol (=)


  True
• Steps involved in algebraic manipulation to solve for a variable.

  1️⃣ Isolate the variable on one side

  2️⃣ Use operations to move terms

  3️⃣ Ensure both sides remain equal
• What is the value of $x$ in the equation $2x =$$4$?


  $2$
• A symbol representing an unknown quantity is called a variable
• To solve the equation $2x +$$3 =$$7$, the first step is to subtract 3
• Variables are typically represented by letters like $x$, $y$, or $z$.


  True
• What is the primary goal of algebraic manipulation when solving equations?

  Isolate the variable
• What is the purpose of a variable in algebra?

  Represent an unknown quantity
• Algebraic manipulation ensures that both sides of an equation remain equal
• Variables are usually represented by letters
• What is the first step in solving an algebraic equation using algebraic manipulation?

  Isolate the variable
• Maintaining equality on both sides of an equation is crucial during algebraic manipulation.


  True