Questions and Answers
What is the correct order of operations in algebra?
The equation 2x + 5 = 11 has no solution.
False
Solve for x in the equation 3x - 2 = 14.
x = 6
To solve the inequality 2x - 3 > 5, we can add ______________ to both sides of the inequality.
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Match the following equations with their solutions:
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What operation should be performed first when evaluating the expression 2 × 3 + 12 - 5?
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The equation x - 2 = 7 has a solution of x = 9.
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What is the value of x in the equation 2x = 16?
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To solve the inequality 3x + 2 > 11, we can subtract ______________ from both sides of the inequality.
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Match the following equations with their solutions:
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Study Notes
Order of Operations in Algebra
- There is a specific order of operations to follow when working with algebraic expressions.
Solving Equations
- The equation 2x + 5 = 11 has no solution, indicating that there is no value of x that satisfies the equation.
- To solve for x in the equation 3x - 2 = 14, we can add 2 to both sides, resulting in 3x = 16, and then divide both sides by 3 to get x = 16/3.
Solving Inequalities
- To solve the inequality 2x - 3 > 5, we can add 3 to both sides of the inequality to get 2x > 8, and then divide both sides by 2 to get x > 4.
Matching Equations with Solutions
- This section requires matching equations with their corresponding solutions, but no specific equations or solutions are provided.
Foundations of Algebra
- Algebra involves the use of variables, constants, and mathematical operations to solve equations and inequalities.
- Variables are letters or symbols that represent unknown values or quantities.
- Constants are numbers or values that do not change.
Order of Operations
- The order of operations is a set of rules used to evaluate expressions containing multiple operations.
- The acronym PEMDAS is commonly used to remember the order:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate from left to right.
- Addition and Subtraction: Evaluate from left to right.
Solving One-Variable Equations
- A one-variable equation is an equation that contains one variable.
- The goal of solving an equation is to isolate the variable on one side of the equation.
- Equations can be solved using inverse operations:
- Addition and subtraction: Use opposite operations to isolate the variable.
- Multiplication and division: Use opposite operations to isolate the variable.
- Equations with variables on one side can be solved by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
Solving One-Variable Inequalities
- A one-variable inequality is an inequality that contains one variable.
- Inequalities can be solved using similar methods as equations, but with some differences:
- When multiplying or dividing both sides by a negative number, the direction of the inequality is reversed.
- Inequalities can be written in different forms, including:
- Less than: <
- Greater than: >
- Less than or equal to: ≤
- Greater than or equal to: ≥
Equations and Inequalities with Variables on Both Sides
- Equations and inequalities can have variables on both sides.
- To solve, use the same methods as above, but combine like terms on each side of the equation or inequality before isolating the variable.
- Simplify the equation or inequality by combining like terms and using inverse operations to isolate the variable.
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Description
Test your understanding of algebra foundations, including the order of operations, solving one-variable equations and inequalities. Solve for x and match equations with their solutions.
