Algebra Foundations

Front

What is the process to solve the equation 2(3x + 4) + 2 = 4 for x?

Back

First, simplify the equation: 2(3x + 4) + 2 = 4 becomes 6x + 8 + 2 = 4. Then, combine like terms: 6x + 10 = 4. Next, isolate x by subtracting 10 from both sides: 6x = -6. Finally, divide by 6: x = -1.

Front

How do you translate the phrase 'The difference of x and 9' into an algebraic expression?

Back

The phrase translates to the expression x - 9.

Front

What is the result of multiplying 2y and 4y?

Back

The result is 8y^2.

Front

How do you express 'The product of 7 and x increased by 6' in algebraic form?

Back

This phrase can be expressed as 7x + 6.

Front

What is the solution for x in the equation 2x + 5 = 12?

Back

To solve for x, subtract 5 from both sides to get 2x = 7, then divide by 2: x = 3.5.

Front

What is the distributive property in algebra?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

What does it mean to isolate a variable in an equation?

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the difference between an expression and an equation?

Back

An expression is a combination of numbers, variables, and operations without an equality sign, while an equation states that two expressions are equal.

Front

How do you solve a linear equation with one variable?

Back

To solve a linear equation, you isolate the variable by performing inverse operations on both sides of the equation until the variable is alone.

Front

What is the importance of combining like terms in algebra?

Back

Combining like terms simplifies expressions and makes it easier to solve equations.