Testinar Grade 8 math

Solving Linear Inequalities

Learn to reason about and solve Grade 8 problems involving Solving Linear Inequalities.

CH03-07 Equations, Inequalities, and Systems
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. Which inequality has the solution graphed below?

    Solving Linear Inequalities visual for G8-C03-T07-Q002
    1. \(x<2\)
    2. \(x>2\)
    3. \(x\leq2\)
    4. \(x\geq2\)

  2. Graph the solution to \(x+4<7\) on a number line. The inequality is:

    Solving Linear Inequalities visual for G8-C03-T07-Q007
    1. \(x<3\)
    2. \(x>3\)
    3. \(x\leq3\)
    4. \(x\geq3\)

  3. Which graph represents \(x\geq-1\)?

    Solving Linear Inequalities visual for G8-C03-T07-Q010
    1. Open circle at \(-1\), ray left
    2. Open circle at \(-1\), ray right
    3. Closed circle at \(-1\), ray right
    4. Closed circle at \(0\), ray right

  4. Solve: \(x+7<10\). Which number line shows the solution?

    Solving Linear Inequalities visual for G8-C03-T07-Q015
    1. \(x<3\)
    2. \(x>3\)
    3. \(x\leq3\)
    4. \(x\geq3\)

  5. Which shows the solution to \(x-3>-7\) on a number line?

    Solving Linear Inequalities visual for G8-C03-T07-Q029
    1. \(x>-4\)
    2. \(x<-4\)
    3. \(x\geq-4\)
    4. \(x\leq-4\)

  6. Which number line shows the solution to \(3-2x>-5\)?

    Solving Linear Inequalities visual for G8-C03-T07-Q038
    1. Closed circle at \(4\), ray left
    2. Open circle at \(4\), ray right
    3. Closed circle at \(4\), ray right
    4. Open circle at \(4\), ray left

  7. Solve and graph: \(-2x+3<-1\). Which describes the graph?

    Solving Linear Inequalities visual for G8-C03-T07-Q045
    1. \(x\geq2\) with closed circle
    2. \(x<2\) with open circle
    3. \(x\leq2\) with closed circle
    4. \(x>2\) with open circle

  8. Solve: \(-2x+5\geq11\)

    1. \(x\geq-3\)
    2. \(x\geq3\)
    3. \(x\leq-3\)
    4. \(x\leq3\)
Teacher and parent reference

Answer key and explanations

  1. A. \(x<2\)

    The open circle at \(2\) means \(2\) is not included. The ray points left to smaller values, so \(x<2\).

  2. A. \(x<3\)

    Subtract \(4\): \(x<3\). The open circle and left-pointing ray show all numbers less than \(3\).

  3. C. Closed circle at \(-1\), ray right

    The inequality \(x\geq-1\) includes \(-1\) (closed circle) and all values greater (ray points right).

  4. A. \(x<3\)

    Subtract \(7\): \(x<3\). The open circle and left ray match this solution.

  5. A. \(x>-4\)

    Add \(3\): \(x>-4\). Open circle at \(-4\) with right ray confirms this.

  6. D. Open circle at \(4\), ray left

    Subtract \(3\): \(-2x>-8\). Divide by \(-2\) (FLIP): \(x<4\). Open circle and left ray.

  7. D. \(x>2\) with open circle

    Subtract \(3\): \(-2x<-4\). Divide by \(-2\) (FLIP): \(x>2\). Open circle and right ray.

  8. C. \(x\leq-3\)

    Subtract \(5\): \(-2x\geq6\). Divide by \(-2\) (and FLIP the inequality): \(x\leq-3\).

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