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NY Regents Algebra I Solving Linear Equations and Inequalities — practice questions — page 2

Explore 57 free Solving Linear Equations and Inequalities questions in NY Regents Algebra I Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Solving Linear Equations and Inequalities questions and exercises with answers

Showing questions 31–57 of 57.

Solve: 8y - 9 = 31.Read the answer and worked solution →Solve: 9x = 8x - 6.Read the answer and worked solution →Solve: 5y - 9 = 8y.Read the answer and worked solution →Solve: 12x = -x + 26.Read the answer and worked solution →Solve: 7x + 5 = 6x + 2.Read the answer and worked solution →Solve: 8n - 4 = -2n + 6.Read the answer and worked solution →Solve: 7a - 3 = 13a + 7.Read the answer and worked solution →Solve: (5/4)x + 6 = (1/4)x - 2.Read the answer and worked solution →Solve: -6(x + 3) = 24.Read the answer and worked solution →Solve: -(y + 9) = 8.Read the answer and worked solution →Solve: 5(a - 3) + 5 = -10.Read the answer and worked solution →Solve: (2/3)(6m - 3) = 8 - m.Read the answer and worked solution →Solve: 8 - 2(3y + 5) = 0.Read the answer and worked solution →Solve: 4(x - 1) - 2 = 5(2x + 3) + 6.Read the answer and worked solution →Solve: 10[3 - 8(2s - 5)] = 15(40 - 5s).Read the answer and worked solution →Solve: 0.36(100n + 5) = 0.6(30n + 15).Read the answer and worked solution →What is a conditional equation?Read the answer and worked solution →What is an identity, and what is its solution?Read the answer and worked solution →Classify the equation 6(2n - 1) + 3 = 2n - 8 + 5(2n + 1), then state the solution.Read the answer and worked solution →Classify the equation 10 + 4(p - 5) = 0, then state the solution.Read the answer and worked solution →Classify the equation 5m + 3(9 + 3m) = 2(7m - 11), then state the solution.Read the answer and worked solution →Solve: (1/6)y - 1/3 = 5/6.Read the answer and worked solution →Solve: 6 = (1/2)v + (2/5)v - (3/4)v.Read the answer and worked solution →Solve: a + 3/4 = (3/8)a - 1/2.Read the answer and worked solution →Solve: -5 = (1/4)(8x + 4).Read the answer and worked solution →Order the equation-solving stepsRead the answer and worked solution →Spot the broken stepRead the answer and worked solution →

Worked practice questions

Solve: 8y - 9 = 31.

  1. y = 5
  2. y = -5
  3. y = 40
  4. y = 22
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Correct answer: A. y = 5

1. The left side is the variable side, so the 9 is out of place there. 2. Add 9 to both sides: 8y equals 40. 3. Divide both sides by 8 to get y equals 5. 4. Check: 8 times 5, minus 9, equals 40 minus 9, which equals 31. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations and Inequalities", section 2.3 Solve Equations with Variables and Constants on Both Sides_

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Solve: 9x = 8x - 6.

  1. x=6
  2. x=-6
  3. x=-2
  4. x=2
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Correct answer: B. x=-6

1. Choose the left side as the variable side, so subtract 8x from both sides to remove x from the right. 2. 9x minus 8x equals -6. 3. Simplify: x equals -6. 4. Check: 9 times -6 equals -54, and 8 times -6 minus 6 also equals -54. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations and Inequalities", section 2.3 Solve Equations with Variables and Constants on Both Sides_

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Solve: 5y - 9 = 8y.

  1. y=3
  2. y=-1
  3. y=-3
  4. y=1
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Correct answer: C. y=-3

1. Leave the constant on the left and move the variable terms to the right by subtracting 5y from both sides. 2. -9 equals 3y after subtracting 5y from both sides. 3. Divide both sides by 3 to get y equals -3. 4. Check: 5 times -3, minus 9, equals -24, and 8 times -3 also equals -24. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations and Inequalities", section 2.3 Solve Equations with Variables and Constants on Both Sides_

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