Algebra 1 Solving Linear Equations in One Variable Quiz: 10 Questions with Explanations

A \(x = 5\)B \(x = 4\)C \(x = 6\)D \(x = \frac{16}{3}\)

Subtract 2 to get 3x = 12, then divide by 3. Adding 2 instead gives 16/3.

A \(x = 7\)B \(x = 18\)C \(x = -7\)D \(x = -24\)

Divide both sides by -3. Forgetting that a negative divided into a positive is negative gives 7.

A \(x = -13\)B \(x = 5\)C \(x = -5\)D \(x = 13\)

Subtract 2x: 9 = x – 4. Add 4: x = 13. A sign slip when moving the -4 gives -13 or 5.

A \(x = 6\)B \(x = 9\)C \(x = 7.5\)D \(x = 24\)

Subtract 6 to get 4x = 24, then divide by 4. Dividing 30 by 4 without subtracting first gives 7.5.

A No solutionB Infinitely many solutionsC Exactly one solution, x = 0D Exactly one solution, x = 4

Distributing gives 4x + 4 = 4x + 4, a true statement for every x.

A \(x = 35\)B \(x = 5.6\)C \(x = 28\)D \(x = 70\)

Multiply both sides by 5/2. Multiplying by 2/5 instead gives 5.6.

A 5 hoursB 6.5 hoursC 8 hoursD 40 hours

Solve 12 + 8h = 52: 8h = 40, so h = 5. Dividing 52 by 8 ignores the fee.

A 9.5 ftB 14 ftC 8.25 ftD 7 ft

Perimeter: 2w + 2(w + 5) = 38, so 4w + 10 = 38 and w = 7. Dividing 38 by 4 forgets the 5.

A \(x = 6.5\)B \(x = 2\)C \(x = 8\)D \(x = 5\)

Distribute: 2x – 6 = 10, so x = 8. Multiplying only the first term gives 2x – 3 = 10.

A \(x = 3\)B \(x = -11\)C \(x = 11\)D \(x = -3\)

The negative sign changes both terms: -x – 4 = 7, so -x = 11 and x = -11.