Advanced Algebra Concepts for 7th Grade

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What is the distributive property of multiplication over addition?

The distributive property states that a(b + c) = ab + ac.

How can you solve an equation with variables on both sides, like 2x + 5 = x + 9?

First, subtract x from both sides to get x + 5 = 9. Then subtract 5 from both sides to get x = 4.

What does it mean for two expressions to be equivalent?

Two expressions are equivalent if they have the same value for all variable assignments.

How do you simplify an expression like 3(x + 4) - 2x?

First, use the distributive property: 3x + 12 - 2x. Then combine like terms: x + 12.

What is the process of finding the greatest common factor (GCF) of two numbers?

List the factors of each number, then find the largest factor that they have in common.

How do you factor the expression x^2 + 5x + 6?

Find two numbers that multiply to 6 and add to 5. These are 2 and 3. So, x^2 + 5x + 6 factors to (x + 2)(x + 3).

How do you solve an equation like 4(x - 2) = 16?

Divide both sides by 4 to get x - 2 = 4. Then add 2 to both sides to get x = 6.

What is a linear equation?

A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.

How do you solve inequalities, such as 3x + 2 < 11?

Subtract 2 from both sides to get 3x < 9, then divide by 3 to find x < 3.

What is the commutative property of addition?

The commutative property of addition states that the order of adding numbers does not change the sum, i.e., a + b = b + a.

How can you express the growth of a pattern using algebra?

Identify the relationship between variables and use an algebraic expression or equation to describe the pattern.

What is a coefficient in an algebraic expression?

A coefficient is a number that is multiplied by a variable in an algebraic expression, e.g., 3 in 3x.

What does it mean for an equation to be 'solvable'?

An equation is 'solvable' if it has a solution, meaning there is a value or values that satisfy the equation.

How do you graph a simple linear equation like y = 2x + 3?

Start by finding the y-intercept (0,3) and then use the slope (2, or rise over run) to plot the next point and draw the line.

What is an algebraic expression?

An algebraic expression is a combination of variables, numbers, and at least one operation (e.g., 3x + 2).