Unit 4 Quiz - Vocabulary Review

________ operations are opposite operations that undo each other.

• inverse

• reciprocal

• subversive

• equivalent

Answer explanation

Inverse operations are mathematical operations that reverse the effect of each other, such as addition and subtraction or multiplication and division. Thus, the correct answer is 'inverse'.

A ____ is a number in an equation that is multiplied by a variable.

• constant term

• expression

• coefficient

• coexistence

Answer explanation

A coefficient is the number that multiplies a variable in an equation, indicating how many times the variable is counted. For example, in 3x, 3 is the coefficient of x.

A ____ is a number in an equation that stands alone; does not multiply by a variable.

• rotation

• reciprocal

• coefficient

• constant term

Answer explanation

A constant term is a number in an equation that does not change and does not multiply by a variable, unlike coefficients which do. Therefore, the correct answer is 'constant term'.

A ___is a value of a variable that makes a true statement when substituted into the equation.

• solution

• constant term

• inverse

• expression

Answer explanation

A solution is a value that, when substituted into an equation, makes the statement true. It directly satisfies the equation, distinguishing it from terms like constant, inverse, or expression.

Which equation has NO solutions?

• 6x - 1 = -1 + 6x

• 6x - 1 = 2 + 3x

• 6x - 1 = 5 + 6x

• 6x - 1 = 12 - 4

Answer explanation

The equation 6x - 1 = 5 + 6x simplifies to -1 = 5, which is a contradiction. Therefore, it has no solutions.

Which equation has INFINITE solutions?

• 3x - 15 = -15 + 3x

• 3x - 15 = 20 + 3x

• 3x - 15 = 10 x - 6

• 3x - 15 = -15 + 2x

Answer explanation

The equation 3x - 15 = -15 + 3x simplifies to 0 = 0, which is always true, indicating infinite solutions. The other equations yield specific values for x, not infinite solutions.

Which equation has ONE solution?

• 2x + 1 = 2x - 1

• 2x + 1 = -1 + 2x

• 2x + 1 = 2x + 6

• 2x + 1 = 6x + 2

Answer explanation

The equation 2x + 1 = 6x + 2 simplifies to 1 = 4x + 2, leading to one solution for x. The other equations either have no solutions or infinitely many solutions.

Select TWO equations that have NO solutions.

• 2(x – 3) = 10x – 6 – 8x

• 3x + 5 = -2

• 5x + 6 = 5x – 4

• 12x + 9 = 8x + 1 + 4x

• 6(x – 11) = 15 – 4x

Answer explanation

The equation 5x + 6 = 5x - 4 simplifies to 6 = -4, which is impossible. Similarly, 12x + 9 = 8x + 1 + 4x simplifies to 9 = 1, also impossible. Thus, both have no solutions.

If you solve an equation and get 0 = 0, what does that mean?

• The equation has infinitely many solutions.

• The equation has only one solution, x = 0.

• The equations has no solution.

• The equation has zero solutions.

Answer explanation

When you solve an equation and get 0 = 0, it indicates that the equation is true for all values of x, meaning there are infinitely many solutions. This is because any value of x satisfies the equation.