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US High School Solving Linear Equations — practice questions

Explore 8 free Solving Linear Equations questions in US High School Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Solving Linear Equations questions and exercises with answers

Showing questions 1–8 of 8.

What makes a particular number a solution of an equation?Read the answer and worked solution →Which form defines a linear equation in one variable?Read the answer and worked solution →What is the first step in the general strategy for solving a linear equation?Read the answer and worked solution →Solve 5(x - 3) + 7 = 2x + 10.Read the answer and worked solution →An equation true for one value of the variable and false for every other is called what?Read the answer and worked solution →Solving 4x + 5 = 4x - 3 removes the variable and leaves 5 equals -3. What is this equation?Read the answer and worked solution →Solve x over 3 plus 1 over 2 equals 5 over 6.Read the answer and worked solution →What is the final step of the general strategy for solving a linear equation?Read the answer and worked solution →

Worked practice questions

What makes a particular number a solution of an equation?

  1. It makes the equation easier to read
  2. It makes the equation a true statement
  3. It appears on the left of the equation
  4. It is the largest number in the equation
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Correct answer: B. It makes the equation a true statement

1. Substitute the number in place of the variable everywhere it appears. 2. Simplify both sides of the equation separately. 3. If the two sides come out equal, the number is a solution, and otherwise it is not. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.1 Use a General Strategy to Solve Linear Equations_

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Which form defines a linear equation in one variable?

  1. ax + b = 0 with a equal to 0
  2. ax squared + b = 0 with a not zero
  3. a over x + b = 0 with a not zero
  4. ax + b = 0 with a not zero
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Correct answer: D. ax + b = 0 with a not zero

1. A linear equation holds one variable raised only to the first power. 2. It can always be rearranged into ax + b = 0 with real numbers a and b. 3. The coefficient a must not be zero, or the variable disappears entirely. 4. A squared term would make it quadratic instead, so that form is ruled out. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.1 Use a General Strategy to Solve Linear Equations_

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What is the first step in the general strategy for solving a linear equation?

  1. Simplify each side as much as possible
  2. Divide both sides by the coefficient
  3. Move every constant to the left side
  4. Check the answer in the original
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Correct answer: A. Simplify each side as much as possible

1. Start by tidying each side on its own before moving anything across. 2. That means clearing parentheses and combining like terms. 3. Only once both sides are simple do you begin collecting variable terms. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.1 Use a General Strategy to Solve Linear Equations_

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More Mathematics topics

Using the Normal DistributionLinear InequalitiesAbsolute Value Equations and InequalitiesMixture and Uniform MotionCompound InequalitiesProblem Solving with EquationsSolving a Formula for a VariableThe Standard Normal Distribution