Solving Linear Equations: Addition and Subtraction Properties of Equality
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Questions and Answers

What is the result of $0.2 \times 100$ according to the information provided?

  • 0.25
  • 20
  • 25 (correct)
  • 5
  • What operation is primarily used in 'LINEAR EQUATIONS PRACTICE' as mentioned in the text?

  • Addition (correct)
  • Multiplication
  • Division
  • Subtraction
  • What is the result of $0.05 + 0.25$ based on the information provided?

  • 0.2 (correct)
  • 25
  • 1
  • 20
  • Which of the following is a false statement according to the text?

    <p>$9 = 4$</p> Signup and view all the answers

    What is the implied calculation for the expression '27' in the provided text?

    <p>$3^3$</p> Signup and view all the answers

    What is the goal of solving a linear equation?

    <p>To find the value of the variable that makes the equation true</p> Signup and view all the answers

    Which property of equality involves adding the same value to both sides of an equation?

    <p>Addition property of equality</p> Signup and view all the answers

    If 2x + 5 = 15, what should be done first to isolate x?

    <p>Subtract 5 from both sides</p> Signup and view all the answers

    What should be multiplied on both sides to clear fractions in an equation?

    <p>The least common denominator (LCD)</p> Signup and view all the answers

    Which step comes first when solving a linear equation in one variable?

    <p>Simplify both sides of the equation</p> Signup and view all the answers

    When is it necessary to clear decimals in an equation?

    <p>When the decimals are not integral</p> Signup and view all the answers

    What is the value of $5(7 + 3)$?

    <p>25</p> Signup and view all the answers

    If $2x - 3 = 7$, what is the value of $x$?

    <p>10</p> Signup and view all the answers

    What type of equation is revealed when solving for a variable and it results in a false statement, such as $7 = 3$?

    <p>Contradiction</p> Signup and view all the answers

    Which of the following is equivalent to $3(4 + 2) - 5$?

    <p>$14 - 5$</p> Signup and view all the answers

    When solving an equation and the variables are eliminated to reveal a true statement, like $13 = 13$, what is this type of equation called?

    <p>Identity</p> Signup and view all the answers

    Solve for $y$ in the equation $2y + 8 = 16$.

    <p>$y = 4$</p> Signup and view all the answers

    In the context of solving equations, what does it mean when a solution checks out?

    <p>The solution has been substituted back into the original equation successfully</p> Signup and view all the answers

    What is the solution to the equation $4(x - 3) = 8$?

    <p>$x = 2$</p> Signup and view all the answers

    What should you do after using multiplication or division properties of equality to solve an equation?

    <p>Substitute your solution into the original equation</p> Signup and view all the answers

    If $3y - 5 = 7$, what is the value of $y$?

    <p>$y = 4$</p> Signup and view all the answers

    If you multiply an equation by its reciprocal, what type of operation are you performing?

    <p>Division</p> Signup and view all the answers

    What is the outcome when solving an equation and it leads to a situation where all real numbers are solutions?

    <p>All real numbers</p> Signup and view all the answers

    What is the solution to the equation $15x - 6 = 9$?

    <p>$x = -\frac{3}{5}$</p> Signup and view all the answers

    What is the solution set of $3(2x - 1) = 5$?

    <p>$x = \frac{4}{3}$</p> Signup and view all the answers

    What does the equation $6(x + 2) = 4(3 - x)$ simplify to?

    <p>$x = -2$</p> Signup and view all the answers

    Which of the following equations has no solution?

    <p>$6(x - 4) + 7 = 8(x + 1)$</p> Signup and view all the answers

    What is the value of $x$ in the equation $\frac{x}{2} - 3 = \frac{3x + 9}{4}$?

    <p>$x = -24$</p> Signup and view all the answers

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