Algebra Class Inequalities and Equations
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Questions and Answers

Solve for x. 76 = 10x - 44

12

Solve for z. -20 = 1/10 z - 22

-20

Which inequality is true when the value of y is -3?

  • *y* - 6 > 4.5
  • -*y* - 6 < 4.5
  • -*y* - 6 < -4.5 (correct)
  • -*y* - 6 > 4.5

    • Which value of x satisfies the equation 1/2(x) - 3/2 = 3/2?

    <p>4</p> Signup and view all the answers

    Which value of x satisfies the equation 4/3(x + 2) + 2/3 = -6?

    <p>-7</p> Signup and view all the answers

    Solve the inequality and graph the solution on the line provided. -16 +4x ≥ 4

    <p>x ≥ 5</p> Signup and view all the answers

    Solve the inequality and graph the solution on the line provided. 7x + 3 > 31

    <p>x &gt; 4</p> Signup and view all the answers

    Graph the line with the equation y = -3x + 3

    <p>This is a linear equation with slope -3 and y-intercept 3. To graph it, start at the y-intercept point (0,3). Then count down 3 units and to the right by 1 unit. Repeat this process to obtain multiple points and connect these points to draw a line</p> Signup and view all the answers

    Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x - 9y = 54

    <p>y = 1/3 <em>x</em> - 6</p> Signup and view all the answers

    Put the following equation of a line into slope-intercept form, simplifying all fractions. 4y - 3x = - 8

    <p>y = 3/4 <em>x</em> - 2</p> Signup and view all the answers

    Put the following equation of a line into slope-intercept form, simplifying all fractions. 9x + 3y = -21

    <p>y = - 3<em>x</em> - 7</p> Signup and view all the answers

    During a snowstorm, snow fell at a constant rate for a number of hours. Then it stopped snowing for a number of hours. Then it started up again at a different constant rate. Brianna made a graph showing the inches of snow on the ground over time using the data that she collected. At what rate was the snow falling during the second snowfall?

    <p>1 inch every 2 hours</p> Signup and view all the answers

    The graph of a function is shown below. What is true about the function between x = -9 and x = -6?

    <p>it is increasing and non-linear</p> Signup and view all the answers

    Starting at noon, Alonso observed the amount of snow on his lawn during a blizzard. He created a graph to represent how many inches of snow were on the lawn at x minutes past noon. What is the meaning of the y-value when x = 60?

    <p>The amount of snow on the lawn at 1 p.m.</p> Signup and view all the answers

    Solve the following system of equations graphically on the set of axes below and state the coordinates of the solution. 1/2 y = -1/2 x + 7 y = x + 4

    <p>(2, 6)</p> Signup and view all the answers

    Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. y ≥ 1/5 x - 1 y ≤ x + 5

    <p>(0, 0)</p> Signup and view all the answers

    Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. y < -1/2 x - 2 y > 2x - 7

    <p>(-4, 0)</p> Signup and view all the answers

    Fill in the blanks below in order to justify whether or not the mapping shown represents a function. The mapping diagram above ______ a function since ______ in ______ has ______.

    <p>does NOT represent, each number, Set B (the output), no mapping</p> Signup and view all the answers

    Which set of ordered pairs does not represent a function?

    <p>{(5, -3), (-2, 3), (-1, 1), (-1, 0)}</p> Signup and view all the answers

    Determine whether the following graph represents a function.

    <p>Not a Function</p> Signup and view all the answers

    Given h(x) = 4x - 4, find h(4).

    <p>12</p> Signup and view all the answers

    Given f(x) = 2x² - 10x + 4, find f(3).

    <p>-8</p> Signup and view all the answers

    Find the range of the function defined by the table below. Express your answer as a set of numbers.

    <p>{ -2 , 3, 5, 8, 9, 10}</p> Signup and view all the answers

    Determine the range of the following graph.

    <p>{-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}</p> Signup and view all the answers

    Combine like terms. -4 - 6x³ + 3y² + 3 + 2x³ + 2 - x³ – 5y²

    <p>-5<em>x</em>³ - 2<em>y</em>² + 1</p> Signup and view all the answers

    Combine like terms. 6y³ - 7x² + 4 + 4x² - 1 - 5y³ + x²

    <p>y³ - 2<em>x</em>² + 3</p> Signup and view all the answers

    Answer the questions about the following polynomial. 5x³ - 1 The expression represents a ______ polynomial with ______ terms. The constant term is ______, the leading term is ______, and the leading coefficient is ______.

    <p>cubic, 2, -1, 5<em>x</em>³, 5</p> Signup and view all the answers

    Answer the questions about the following polynomial. x - 1/9

    The expression represents a ______ polynomial with ______ terms. The constant term is ______, the leading term is ______, and the leading coefficient is ______.

    <p>linear, 2, -1/9, x, 1</p> Signup and view all the answers

    Perform the operation. (5x² + 10x - 4) - (-7x² + 10)

    <p>12<em>x</em>² + 10<em>x</em> - 14</p> Signup and view all the answers

    Perform the operation. ( 3x + 9) + ( 3x² - x + 6)

    <p>3<em>x</em>² + 2<em>x</em> + 15</p> Signup and view all the answers

    Perform the operation. (-x² + 2x + 3) - (-8x + 7)

    <p>-<em>x</em>² + 10<em>x</em> - 4</p> Signup and view all the answers

    Determine the domain of the following graph.

    <p>All real numbers from -10 to 12, or -10 ≤ <em>x</em> ≤ 12</p> Signup and view all the answers

    Determine the domain on which the following function is decreasing.

    <p>0 ≤ <em>x</em> ≤ 3</p> Signup and view all the answers

    The graph of y = f(x) is shown below. Find all values of x for which f(x) < 0.

    <p>-9 &lt; x &lt; -5</p> Signup and view all the answers

    Graph the following features: • Y-intercept = 1 • Slope = -2

    <p>To graph a line, you need two points. A y-intercept of 1 means the graph passes through the point (0,1). From there, the slope of -2 means to move down 2 units and to the right by 1 unit. This will give you another point and you can draw a line connecting the two points.</p> Signup and view all the answers

    Below are two inequalities and the graphs of their lines without the shading. By imagining where the shading should be, identify which point would satisfy BOTH inequalities. y < 1/6 x + 1
    y > x + 1

    <p>(-10, 6)</p> Signup and view all the answers

    Below are two inequalities and the graphs of their lines without the shading. By imagining where the shading should be, identify which point would satisfy BOTH inequalities. y < -x + 5 y > 5x - 3

    <p>(3, 1)</p> Signup and view all the answers

    Express in simplest radical form: √48

    <p>4√3</p> Signup and view all the answers

    Express in simplest radical form. -7√54 + 3√150

    <p>11√6</p> Signup and view all the answers

    Express in simplest radical form. 7√6 - √6

    <p>6√6</p> Signup and view all the answers

    Expand the expression to a polynomial in standard form. (x - 9)(2x² - x + 3)

    <p>2<em>x</em>³ - 19<em>x</em>² +12<em>x</em> - 27</p> Signup and view all the answers

    Expand the expression to a polynomial in standard form. ( 4x - 3)(x² - 2x - 8 )

    <p>4<em>x</em>³ -11<em>x</em>² - 26<em>x</em> + 24</p> Signup and view all the answers

    Study Notes

    Algebra Problems

    • Solve for x: 76 = 10x - 44 (Answer: x = 12).

    • Solve for z: -20 = z/10 - 22 (Answer: z = -20)

    • Inequality when w = 8: Which inequality is true when w = 8?

      • A. w - 6 > 4.5 → 8 - 6 > 4.5 → 2 > 4.5 (False)
      • B. w - 6 < 4.5 → 8 - 6 < 4.5 → 2 < 4.5 (True)
      • C. -w - 6 > -4.5 (Not applicable given w = 8)

    • Inequality when y is -3: Which inequality is true when y is -3?

      • A. -y - 6 < 4.5 → -(-3) - 6 < 4.5 → 3 - 6 < 4.5 → -3 < 4.5 (True)
      • B. -y - 6 < -4.5 → -(-3) - 6 < -4.5 → 3 - 6 < -4.5 → -3 < -4.5 (False)
      • C. y - 6 > 4.5 → -3 - 6 > 4.5 → -9 > 4.5 (False)
      • D. -y - 6 > 4.5 → -(-3) - 6 > 4.5 → 3 - 6 > 4.5 → -3 > 4.5 (False)

    • Inequality when t is -12: Which inequality is true when t = -12?

      • A. t +1.5 < -8 → -12 + 1.5 < -8 → -10.5 < -8 (True)
      • B. t +1.5 > -8 → -12 + 1.5 > -8 → -10.5 > -8 (False)
      • C. t +1.5 < 8 → -12 + 1.5 < 8 → -10.5 < 8 (True)
      • D. t + 1.5 > 8 → -12 + 1.5 > 8 → -10.5 > 8 (False)

    • Solve for x: 4/5(x+2)=-6 (Answer: x = -8)

    • Solve Inequality: -16 + 4x ≥ 4

      • (Answer: x ≥ 5).

    • Graph Inequalities Solve and graph inequalities using these steps:

      1. Isolate the variable
      2. Determine the direction of the inequality symbol
      3. Graph your solution labeling your points.

    Other Math Problems

    • Slope Intercept Form: Convert equations to slope-intercept form (y = mx + b).

    • Graphing Lines: Graph linear equations on coordinate planes.

    • Simultaneous Equations: Find solutions to systems of equations graphically.

    • Inequalities: Graph systems of inequalities, finding points that satisfy both inequalities by shading appropriately.

    • Snowfall Rate: If snow fell at a constant rate for hours and then changed rates, determining the rate of the second snowfall by analyzing a graph. (e.g. 2 inches every 3 hours).

    • Function Behavior: Understanding increasing and decreasing intervals from graph information/ data).

    • Domain of a Graph: Determining the x-values for which a function is defined on a graph.

    • Function Values: Evaluating functions at specific input values.

    • Combining Like Terms: Combine constant, variables and exponents to simplify expressions.

    • Polynomial Terminology: Polynomials are expressions with multiple terms consisting of variables raised to powers and constants. There are different types (quadratic, cubic, etc.) and components (constants, leading term).

    • Simplifying Radicals: Simplify radical expressions.

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    Description

    Test your knowledge of solving equations and inequalities in this algebra quiz. You'll tackle problems involving finding values for variables like x, z, w, y, and t. Get ready to identify true inequalities and solve for unknowns!

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