About Solving Linear Inequalities Part 2:

When we solve a multi-step linear inequality, we first simplify each side. We will clear any parentheses, decimals, or fractions, and then combine any like terms. Once this is done, we will move all the variable terms to one side and the constants to the other. Lastly, we will isolate the variable term. Keep in mind that if we multiply or divide both sides by a negative number, we must flip the direction of the inequality symbol.

Test Objectives
  • Demonstrate the ability to solve a multi-step linear inequality
  • Demonstrate the ability to solve a three-part linear inequality
  • Demonstrate the ability to write the solution in interval notation
  • Demonstrate the ability to graph an interval on the number line
Solving Inequalities Part 2 Practice Test:

#1:

Instructions: Solve each inequality, write the answer in interval notation, and graph each interval on the number line.

a) 3(5 - 5x) - 3(2 - 6x) < -x + 3x

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#2:

Instructions: Solve each inequality, write the answer in interval notation, and graph each interval on the number line.

a) -2(1 + 5x) ≥ 3 + 3(1 - 6x)

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#3:

Instructions: Solve each inequality, write the answer in interval notation, and graph each interval on the number line.

a) -(1 + 2x) > -6(x - 4) - 1

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#4:

Instructions: Solve each inequality, write the answer in interval notation, and graph each interval on the number line.

a) -46 < 4x - 6 ≤ -26

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#5:

Instructions: Solve each inequality, write the answer in interval notation, and graph each interval on the number line.

a) -4 ≤ x + 3 ≤ 2

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Written Solutions:

#1:

Solutions:

a) x < -9 : (-∞,-9)solution x is less than -9

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#2:

Solutions:

a) x ≥ 1 : [1,∞)solution x is greater than or equal to 1

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#3:

Solutions:

a) x > 6 : (6,∞)solution x is greater than 6

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#4:

Solutions:

a) -10 < x ≤ -5 : (-10,-5]solution x is greater than -10 and x is less than or equal to -5

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#5:

Solutions:

a) -7 ≤ x ≤ -1 : [-7,-1]solution x is greater than or equal to -7 and x is less than or equal to -1

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