Solving Equations with One Variable
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Questions and Answers

What is the first step in solving the equation (x/4) + 6 = 10?

  • Isolate the variable x
  • Multiply both sides by 4
  • Subtract 6 from both sides (correct)
  • Add 6 to both sides

What does isolating the variable x in the equation (x/3) + 2 = 5 involve?

  • Adding 2 to both sides
  • Subtracting 2 from both sides (correct)
  • Multiplying both sides by 3
  • Dividing both sides by 3

In the equation (x/5) + 1 = 3, what value will x have after solving it?

  • 10
  • 15
  • 25
  • 20 (correct)

When solving (x/2) + 4 = 12, what operation should you perform first?

<p>Subtract 4 from both sides (C)</p> Signup and view all the answers

What happens to the equation when you multiply both sides by the denominator in the equation x/6 + 3 = 7?

<p>It results in an easier equation to solve (A)</p> Signup and view all the answers

Which of these is an example of an error when solving an equation?

<p>Incorrectly isolating the variable (B)</p> Signup and view all the answers

Solving (x/8) = 4 requires which final operation to find x?

<p>Multiplying both sides by 8 (B)</p> Signup and view all the answers

If x = 15 solves the equation (x/3) + 5 = 10, what step verifies that x is correct?

<p>Substituting 15 back into the original equation (B)</p> Signup and view all the answers

Flashcards

Solving Equations

Finding the value of a variable (like 'x') that makes an equation true.

Inverse Operations

Operations that undo each other, like addition and subtraction, or multiplication and division.

Isolate the variable

Get the variable (often 'x') all by itself on one side of the equation.

Equation

A statement that two expressions are equal.

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Solving (x/a + b = c)

To find the value of 'x' in an equation where 'x' is divided by 'a', then added to 'b' and equals 'c'.

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Variable

A letter or symbol that represents an unknown value.

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Constant

A fixed numerical value in an equation.

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Check Solution

Substituting the found value (of the variable) back into the original equation to make sure it is correct.

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Study Notes

Solving Equations with One Variable

  • Equations are statements that show two expressions are equal.
  • To solve an equation, you isolate the variable (usually 'x') on one side of the equation. This is done using inverse operations.
  • Inverse operations undo each other: addition and subtraction are inverse operations; multiplication and division are inverse operations.

Solving Equations of the Form (x/a + b = c)

  • The first step to solving an equation of the form (x/a + b = c) is to isolate the term with 'x'.
  • Subtraction is used to move the constant 'b': Subtract 'b' from both sides of the equation.
  • The equation will now be in the form (x/a = c - b).
  • Multiplication is used to eliminate the fraction. Multiply both sides of the equation by the denominator 'a'.
  • The equation will now be in the form x = a * (c - b).
  • Simplify the right side of the equation to isolate x.
  • The answer is the value of x.

Example Steps for Solving Equations

  • Problem: (x / 5) + 3 = 8
    1. Subtract 3 from both sides: This isolates (x / 5): (x / 5) = 8 - 3
    1. Simplify: (x / 5) = 5
    1. Multiply both sides by 5: This isolates x: x = 5 * 5
    1. Simplify: x = 25
  • Solution: x = 25

Important Concepts

  • Equality: The equals sign (=) indicates that the expressions on both sides of the equation have the same value.
  • Variables: Symbols, often 'x,' represent unknown values.
  • Constants: Fixed numerical values.
  • Inverse Operations: Operations that cancel each other out.
  • Isolate the Variable: The goal is to get the variable (x) by itself on one side of the equation.
  • Equivalent Equations: Equations that have the same solutions.
  • Checking Solutions: Substitute the solution back into the original equation to ensure it holds true.

Common Errors and Pitfalls

  • Forgetting to apply the same operation to both sides of the equation.
  • Making algebraic errors while simplifying.
  • Mistakes in signs (+ or -).
  • Not properly isolating variables or constants during the solution steps.

Practice Problems

  • (Illustrative problems solving for x in various equations would be helpful here from the worksheet).
  • Understanding steps for isolating x for equations in the form ax + b = c
  • Solving for x for equations in the form (x/a) +b = c

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Description

This quiz focuses on solving equations with one variable, particularly of the form (x/a + b = c). Participants will learn how to isolate the variable by using inverse operations like addition and subtraction, as well as multiplication and division. Practice solving these equations to improve your algebra skills.

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