Core Skill Review: U1 Algebraic Concepts

Front

Which property is demonstrated by (2 + x) + 5 ⇒ 2 + (x + 5)?

Back

Associative Property: This property states that the way in which numbers are grouped in addition or multiplication does not change their sum or product.

Front

If x + y = 10 and x - y = 4, find the value of x.

Back

x = 7. By solving the system of equations, we can find the value of x.

Front

If 2x + 1 = 7, what is the value of 4x + 2?

Back

4x + 2 = 14. First, solve for x, then substitute to find the expression.

Front

What is the expression for '5 less than half the sum of a and b'?

Back

(a + b) / 2 - 5. This expression represents the mathematical translation of the given phrase.

Front

If 3x + 2 = 14, what is the value of 6x + 4?

Back

6x + 4 = 20. By solving for x, we can find the value of the expression.

Front

Define the Commutative Property of Addition.

Back

The Commutative Property states that changing the order of the addends does not change the sum. For example, a + b = b + a.

Front

Define the Distributive Property.

Back

The Distributive Property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

What is the solution to the equation 5x - 3 = 12?

Back

x = 3. Add 3 to both sides and then divide by 5.

Front

What is the value of x in the equation 4(x - 2) = 16?

Back

x = 6. First, divide both sides by 4, then add 2.

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.