Solving Basic Algebra Equations Practice Questions
Solving equations is not very different from working with numerical or algebraic expressions. An equation is a mathematical statement where two expressions are set equal to each other. Using logic and mathematical operations, you can manipulate the equation to find a solution. Simply put, that is what you have done when you have the variable on one side of the equal sign and a number on the other. The answer explanations will show and identify all the steps you will need to solve basic equations. There will be different solutions to similar problems to show a variety of methods for solving equations. But they all rely on the same rules. Look over the Tips for Solving Basic Equations before you begin this lesson's questions.
Tips for Solving Basic Equations
- If a number is being added to or subtracted from a term on one side of an equation, you can eliminate that number by performing the inverse operation.
- The inverse of addition is subtraction. The inverse of subtraction is addition. If you add or subtract an amount from one side of the equation, you must do the same to the other side to maintain the equality.
- The inverse of multiplication is division. If a variable is being multiplied by a coefficient, you can eliminate the coefficient by dividing both sides of the equation by that coefficient, leaving you with just one of the variables. If a is a number ≠ 0, then ax ÷ a = x.
- The inverse of division is multiplication. If a number is dividing a variable, you can multiply the term by the number, leaving you with one of the variables. If b is a number ≠ 0, then .
- You can perform any operation to a term in an equation. Just remember that you must do it to both sides. When you have the variable isolated on one side of the equation, the value on the other side is your solution.
- a + 21 = 32
- x – 5 = 32
- y + 17 = –12
- b – 15 = 71
- 12 – c = –9
- s– –4 = –1 a + 1
- m + 2(5 – 24) = –76
- 2a = 24
- 4x = –20
- –3y = 18
- 27b = 9
- 45r = –30
- 0.2c = 5.8
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- After putting 324 teddy bears into packing crates, there were 54 crates filled with bears. If each crate contained the same number of bears, how many bears were in each packing crate?
- Only 3% of turtle hatchlings will live to become breeding adults. How many turtles must have been born if the current number of breeding adults is 1,200?
- This year, a farmer planted 300 acres of corn. This was 1.5 times as many acres as he planted last year. How many acres did he plant this year?
- A business executive received a $6,000 bonus check from her company at the end of the year. This was 5% of her annual salary. How much was her annual salary before receiving the bonus?
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