Solving Linear Inequalities and Equations in One Variable

Solve for x

3x − 8 ≥ 4(x − 1.5)

• x ≥ 3.5

• x ≤ 3.5

• x ≥ −2

• x ≤ −2

Solve the inequality

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Write an inequality for Graph 3.

• x ≤ -2 AND x > 5

• x ≤ -2 OR x > 5

• x ≥ -2 OR x < 5

• -2 ≤ x < 5

Pick the correct letter for:
6 > x

• A

• B

• C

• D

Solve the equation shown.

Show the work you do in finding your final answer on the paper provided.

Mathematical Equivalence

ON

Answer explanation

Write an inequality for Graph 3.

• x ≤ -2 AND x > 5

• x ≤ -2 OR x > 5

• x ≥ -2 OR x < 5

• -2 ≤ x < 5

Find the Error
What error did the student make when solving the equation:
⅕x + 6 = ⅗x + 5
1x + 6 = 3x + 5
-2x + 6 = 5
-2x = -1
x = 1/2

• The student found an incorrect common denominator

• The student did not multiply all terms by the common denominator

• The student did not use opposite operations appropriately

• The student did not correctly eliminate the variable from one side of the equation

Solve the following equation for x:
4(2x - 3) = 6x + 2

• x = 5/2

• x = 7

• x = 1

• no solution

Which of the following equations would have infinite solutions?

• 3x + 9 = 2x + 9

• 8x = 8x + 4

• 3(4x + 4) = 12x +4

• -5x + 10 = 10 - 5x

conditions given to variables, often expressed as linear inequalities

• constraints

• elimination method

• vertex