Solving Linear Equations in One Variable

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Questions and Answers

What is the goal of solving linear equations in one variable?

  • To find the value of the variable that is always one
  • To find the value of the variable that is always zero
  • To find the value of the variable that satisfies the given equation (correct)
  • To find the value of the variable that does not satisfy the equation

In the equation X + 7 = 12, what is the first step to solve for X?

  • Transposing 7 to the other side of the equation, changing its sign to negative (correct)
  • Transposing 7 to the other side of the equation, changing its sign to positive
  • Transposing 12 to the other side of the equation, changing its sign to negative
  • Transposing 7 to the same side of the equation

What is the value of X in the equation 2X + 3 = 9?

  • X = 4
  • X = 2
  • X = 3 (correct)
  • X = 5

In the equation 3(X + 2) = 2, what is the first step to solve for X?

<p>Using the distributive property to multiply 3 with the terms inside the parenthesis (B)</p> Signup and view all the answers

What is the value of X in the equation (2X - 3)/6 = X + 4?

<p>X = -27/4 (B)</p> Signup and view all the answers

What is the purpose of cross-multiplication in the equation (2X - 3)/6 = X + 4?

<p>To eliminate the denominator (D)</p> Signup and view all the answers

What is represented by the two bars, | |?

<p>The distance of a number from zero on the number line (B)</p> Signup and view all the answers

What is the absolute value of the number -5?

<p>5 (C)</p> Signup and view all the answers

What is the absolute value of the expression |-8| + 10?

<p>18 (C)</p> Signup and view all the answers

What is the absolute value of the expression |-15| - |-3|?

<p>12 (D)</p> Signup and view all the answers

What is the purpose of finding the absolute value of a number?

<p>To find the distance of a number from zero on the number line (B)</p> Signup and view all the answers

What is the absolute value of the expression |14| + |-6|?

<p>20 (A)</p> Signup and view all the answers

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Study Notes

Solving Linear Equations in One Variable

  • The goal is to find the value of the variable that satisfies the given equation, also known as the solution.

Example 1: X + 7 = 12

  • To solve, transpose 7 to the other side of the equation, changing its sign to negative.
  • Simplify the equation: 12 - 7 = 5, so the value of x is 5.

Example 2: 2X + 3 = 9

  • Transpose 3 to the other side, changing its sign to negative.
  • Simplify the equation: 2X = 9 - 3, which equals 2X = 6.
  • Divide both sides by 2 to solve for x: x = 6 ÷ 2 = 3.

Example 3: 3(X + 2) = 2

  • Use the distributive property to multiply 3 with the terms inside the parenthesis.
  • Simplify the equation: 3X + 6 = 2, which equals 3X = 2 - 6.
  • Divide both sides by 3 to solve for x: x = -4 ÷ 3 = -4/3.

Example 4: (2X - 3)/6 = X + 4

  • Method 1: Cross-multiplication

    • Express the right side of the equation as a fraction: X + 4 = X/1 + 4/1.
    • Cross-multiply: 6(X + 4) = 2X - 3.
    • Simplify the equation: 6X + 24 = 2X - 3, which equals 4X = -27.
    • Divide both sides by 4 to solve for x: x = -27 ÷ 4 = -27/4.

  • Method 2: Multiply the entire equation by 6 to eliminate the denominator.

    • Simplify the equation: 2X - 3 = 6X + 24.
    • Combine like terms: -4X = 27.
    • Divide both sides by -4 to solve for x: x = -27 ÷ 4 = -27/4.

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