One Variable Equations

When attempting to do his/her homework, a student uses the addition property of equality to solve for a below. Which statement BEST applies to the sample below? A. The student failed to keep both sides of the equation balanced. B. The student's final answer does not have the variable a isolated. C. The use of the addition property of equality is sound, and the answer is correct. D. The student should have added 3 to the left side of the equation rather than subtracting.

A

Which of the following is an example of a valid use of the addition property of equality? A. to isolate the g in the equation g - 4 = 0, add 4 to both sides of the equation B. to isolate the g in the equation g - 4 = 0, subtract 4 from both sides of the equation C. to isolate the g in the equation -4g = 0, add 4 to both sides of the equation D. to isolate the g in the equation -4g = 0, subtract 4 from both sides of the equation

A

Which property of equality would be used to isolate the variable a in this equation? a-4=12 A. addition property of equality B. subtraction property of equality C. multiplication property of equality D. division property of equality

A

Which property of equality would be used to isolate the variable x in this equation? z-8=14 A. addition property of equality B. subtraction property of equality C. multiplication property of equality D. division property of equality

A

Which property would be used to isolate the variable h in this equation? h + 12 = 26 A. addition property of equality B. commutative property of addition C. multiplication property of equality D. division property of equality

A. addition property of equality

Solve for x in the equation -2/5x=12

A. -30

Which of the following BEST summarizes how to solve for the variable x in the equation below, and which rule was used to do so? 2/3x=-2 A. multiply by 3/2 on both sides of the equation by the addition property of equality B. multiply by 3/2 on both sides of the equation by the multiplication property of equality C. add -2 to both sides of the equation by the addition property of equality D. add -2 to both sides of the equation by the multiplication property of equality

B

When attempting to do her homework, Katie incorrectly uses the multiplication property of equality. Which of the statements below describes Katie's error? A. Katie should have used the addition property of equality instead. B. Katie did not keep the equation balanced because she did not multiply both sides of the equation by the same value. C. Katie did not isolate the variable r. D. Katie should have multiplied both sides of the equation by 2/3

B. Katie did not keep the equation balanced because she did not multiply both sides of the equation by the same value.

A student is asked to solve the equation below and to justify his/her steps. Identify what, if anything, is incorrect in the math or justification. j - 8 = -13 A. The student mislabeled the work in the second step as "Addition property of equality." B. The student improperly applied the addition property of equality in the second step. C. The student computed the sums improperly to arrive at an erroneous answer in step 3. D. There is no error. The student's justification is correct.

B. The student improperly applied the addition property of equality in the second step.

Which of the following BEST describes how to use the multiplication property of equality to isolate the variable n below? 12/13n = -31/16 A. multiply both sides of the equation by 12/13 B. multiply both sides of the equation by 13/12 C. multiply only the left side of the equation by 12/13 D. divide only the left side of the equation by 13/12

B. multiply both sides of the equation by 13/12

Which of the following BEST describes how use of the multiplication property of equality to isolate the variable x below? -3x = 12 A. multiply by -3 on both sides of the equation B. multiply by -1/3 on both sides of the equation C. add 3 to both sides of the equation D. multiply by 1/3 on both sides of the equation

B. multiply by -1/3 on both sides of the equation

Which of the following is an example of a valid use of the addition property of equality? A. to isolate the z in the equation z + 8 = 14, add 8 to both sides of the equation B. to isolate the z in the equation z + 8 = 14, add -8 to both sides of the equation C. to isolate the z in the equation 8z = 14, add 8 to both sides of the equation D. to isolate the z in the equation 8z = 14, subtract 8 from both sides of the equation

B. to isolate the z in the equation z + 8 = 14, add -8 to both sides of the equation

A student is asked to solve the equation below and to justify her/his steps. Identify what, if anything, is incorrect in her/his math or justification. x+4=-8 A. The student mislabeled the work in the step 2 as "Addition property of equality." B. The student improperly applied the "Addition property of equality" in step 2. C. The student added improperly and got the wrong answer in step 3. D. There is no error. The student's justification is correct.

C

When attempting to do his homework, Mark incorrectly uses the addition property of equality below. Which statement would correct Mark's error? A. To balance the equation, Mark should also subtract 2 from the right side of the equation in step 2. B. To balance the equation, Mark should also subtract 2 from both sides of the equation in step 2. C. To balance the equation, Mark should also subtract 8 from the right side of the equation in step 2. D. To balance the equation, Mark should also add 8 to both sides of the equation in step 2.

C

Which of the following best describes how to use of the addition property of equality to isolate the variable x below? 5 = x - 2 A. add 5 to both sides of the equation B. subtract 5 from both sides of the equation C. add 2 to both sides of the equation D. subtract 2 from both sides of the equation

C. add 2 to both sides of the equation

Which property would be used to isolate the variable j in this equation? 7*j=49 A. addition property of equality B. commutative property of addition C. multiplication property of equality D. distributive property

C. multiplication property of equality

A student is asked to solve the equation below and to justify her/his steps. Identify what, if anything, is incorrect in her/his math or justification. z-3=11 A. The student mislabeled the work in the second step as "Addition property of equality." B. The student improperly applied the addition property of equality in the second step. C. The student computed the sums improperly to arrive at an erroneous answer in step 3. D. There is no error. The student's justification is correct.

D

Which of the following BEST summarizes how to use the multiplication property of equality to isolate the variable p below? -1/2p=4 A. divide only the right side of the equation by 2 B. multiply only the right side of the equation by 2 C. divide both sides of the equation by -2 D. multiply both sides of the equation by -2

D

Which of the following BEST summarizes how to solve for the variable x in the equation below, and which rule was used to do so? -3 = 4x A. add -3 to both sides of the equation by the addition property of equality B. add -3 to both sides of the equation by the multiplication property of equality C. multiply by 1/4 on both sides of the equation by the addition property of equality D. multiply by 1/4 on both sides of the equation by the multiplication property of equality

D. multiply by 1/4 on both sides of the equation by the multiplication property of equality

Which of the following is an example of a valid use of the multiplication property of equality? A. to isolate t in the equation t + 8 = -4, multiply both sides of the equation by 8 B. to isolate t in the equation t + 8 = -4, divide both sides of the equation by 8 C. to isolate t in the equation 8t = -4, multiply both sides of the equation by 1/8 D. to isolate t in the equation 8t = -4, divide both sides of the equation by 1/8

c. to isolate t in the equation 8t = -4, multiply both sides of the equation by 1/8