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

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 1–30 of 57.

In algebra, what is a value of a variable called if it makes an equation a true statement when substituted in?Read the answer and worked solution →The Subtraction Property of Equality states that if a equals b, what must also be true for any number c?Read the answer and worked solution →Solve: y + 37 = -13.Read the answer and worked solution →The Addition Property of Equality states that if a equals b, what must also be true for any number c?Read the answer and worked solution →Solve: a - 28 = -37.Read the answer and worked solution →Solve: x - 5/8 = 3/4.Read the answer and worked solution →Solve: n - 0.63 = -4.2.Read the answer and worked solution →Solve: 9x - 5 - 8x - 6 = 7.Read the answer and worked solution →Solve: 5(n - 4) - 4n = -8.Read the answer and worked solution →Solve: 3(2y - 1) - 5y = 2(y + 1) - 2(y + 3).Read the answer and worked solution →Translate and solve: Eleven more than x is equal to 54.Read the answer and worked solution →Translate and solve: The difference of 12t and 11t is -14.Read the answer and worked solution →Randell paid $28,675 for his new car, which was $875 less than the sticker price. What was the sticker price?Read the answer and worked solution →The Division Property of Equality states that if a equals b and c is not zero, what must also be true?Read the answer and worked solution →Solve: 5x = -27.Read the answer and worked solution →The Multiplication Property of Equality states that if a equals b, what must also be true for any number c?Read the answer and worked solution →Solve: y / -7 = -14.Read the answer and worked solution →Solve: -n = 9.Read the answer and worked solution →Solve: (3/4)x = 12.Read the answer and worked solution →Solve: 8/15 = -(4/5)x.Read the answer and worked solution →Solve: 14 - 23 = 12y - 4y - 5y.Read the answer and worked solution →Solve: -4(a - 3) - 7 = 25.Read the answer and worked solution →Translate and solve: The number 143 is the product of -11 and y.Read the answer and worked solution →Translate and solve: n divided by 8 is -32.Read the answer and worked solution →Translate and solve: The quotient of y and -4 is 68.Read the answer and worked solution →Translate and solve: Three-fourths of p is 18.Read the answer and worked solution →Translate and solve: The sum of three-eighths and x is one-half.Read the answer and worked solution →Denae bought 6 pounds of grapes for $10.74. What was the cost of one pound of grapes?Read the answer and worked solution →Andreas bought a used car for $12,000, which was three-fourths of the original price. What was the original price?Read the answer and worked solution →Solve: 7x + 8 = -13.Read the answer and worked solution →

Worked practice questions

In algebra, what is a value of a variable called if it makes an equation a true statement when substituted in?

  1. A solution
  2. A constant
  3. An expression
  4. A coefficient
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Correct answer: A. A solution

1. The definition names the value that makes an equation a true statement, once substituted in, a solution. 2. A constant is a fixed number appearing in the equation, not a value found by solving it. 3. An expression or a coefficient can appear inside the equation, but neither word describes the value being sought. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations and Inequalities", section 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality_

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The Subtraction Property of Equality states that if a equals b, what must also be true for any number c?

  1. a-c=b+c
  2. a+c=b-c
  3. a-c=b-c
  4. a*c=b*c
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Correct answer: C. a-c=b-c

1. The property allows the same quantity c to be subtracted from both sides of an equation without changing whether it is true. 2. If a equals b, subtracting c from a and from b keeps both sides equal to each other. 3. Subtracting c from only one side, or multiplying both sides instead, would not preserve the equality in the same way. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations and Inequalities", section 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality_

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Solve: y + 37 = -13.

  1. y = -76
  2. y = 24
  3. y = 50
  4. y = -50
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Correct answer: D. y = -50

1. To isolate y, subtract 37 from both sides using the Subtraction Property of Equality. 2. y plus 37 minus 37 equals -13 minus 37. 3. Simplify both sides: y equals -50. 4. Check: -50 plus 37 equals -13, which matches the original equation. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations and Inequalities", section 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality_

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More Mathematics topics

Systems of Linear EquationsGraphing Linear EquationsPolynomials and ExponentsRational Expressions and EquationsModeling with Linear EquationsSolve Equations Using Properties of EqualitySolve Systems of Equations by GraphingUse a General Strategy to Solve Linear Equations