2.2.4 Solving linear inequalities in one or two variables

• What are the comparison symbols used in linear inequalities?

  > ||| < ||| ≥ ||| ≤
• The solution region in a linear inequality graph satisfies the original inequality.


  True
• How can you find the slope of the line y = 3x + 5?

  • The slope of the line is 3, which is the coefficient of x
• What does graphing a linear inequality in two variables help visualize?

  Solutions in a region
• What is the next step after subtracting 5 from both sides of 2x + 5 > 11?

  Divide by 2
• What are the inequality symbols used in linear inequalities in two variables?

  $\gt, \lt, \geq, \leq$
• Steps to solve linear inequalities in the correct order:

  1️⃣ Simplify both sides

  2️⃣ Isolate the variable

  3️⃣ Solve for the variable
• The solutions to a linear inequality in two variables are all the points within the defined region.


  True
• What are the key points on the graph that define the region satisfying the inequality?

  • Point (0,0) is in the original inequality
  • Point (0,-5) is on the boundary line
  • Point (10,-5) is also on the boundary line
• Steps to solve 4x - 2 + 6x < 28 in the correct order:

  1️⃣ Combine like terms

  2️⃣ Add 2 to both sides

  3️⃣ Divide by 10
• Combining like terms is a simplification step in solving linear inequalities.

  True
• Combining like terms in 4x - 2 + 6x < 28 results in 10x - 2 < 28.

  True
• Linear inequalities in two variables define a region on a coordinate plane rather than a number line.


  True
• What is the inequality that defines the region of the plane that satisfies the given condition?

  $y < \frac{1}{2}x - 5$
• What is the equation of the line y = x^2 - 2?

  y = x^2 - 2
• Dashed lines in the graph of a system of inequalities indicate strict inequalities such as > or <.


  True
• How does the graph of the inequality compare to the boundary line?

  • The region satisfying the inequality is below the boundary line
  • The inequality is a strict inequality, so the boundary line itself is not part of the solution region
• What region should be shaded when (0,0) does not satisfy y < \frac{1}{2}x - 5</latex>?

  Below the line
• How does the graph of y = 3x + 5 compare to the graph of y = x^2 - 2?

  • The graph of y = 3x + 5 is a straight line, while the graph of y = x^2 - 2 is a parabola
  • The line y = 3x + 5 has a constant slope of 3, while the parabola y = x^2 - 2 has a changing slope
• What type of line should be used when graphing an inequality with a < symbol?

  Dotted line
• How can you find the y-intercept of the line y = 3x + 5?

  • The y-intercept of the line is 5, which is the constant term
• When multiplying or dividing by a negative number, you must reverse the inequality sign.


  True
• A system of inequalities has only one solution region.

  True
• A solid line is used when graphing an inequality with ≤ or ≥.


  True
• Linear inequalities have one solution.

  False
• How do the graphs of y = 3x + 5 and y = x^2 - 2 differ in their shapes?

  The graph of y = 3x + 5 is a straight line, while the graph of y = x^2 - 2 is a parabola
• What is the solution region in the graph of a system of inequalities?

  Overlapping shaded area
• What is the slope of the line y = x^2 - 2?

  The slope is not constant, it changes at different points on the line
• The boundary lines in the graph of a system of inequalities are always straight lines.


  True
• What is the equation of the boundary line that separates the region satisfying the inequality from the region that does not?

  $y =$$\frac{1}{2}x - 5$
• What is the equation of the line y = 3x + 5?

  • The equation of the line is y = 3x + 5
• What is the y-intercept of the line y = x^2 - 2?

  -2
• What must you do to the inequality sign if you multiply or divide by a negative number?

  Reverse the sign