Basic Algebra Review

Front

What is the distributive property in algebra?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you simplify the expression 3(2y - 7)?

Back

To simplify 3(2y - 7), apply the distributive property: 3 * 2y - 3 * 7 = 6y - 21.

Front

What is the process to solve the equation 8x - 10 = -34 for x?

Back

To solve for x, first add 10 to both sides: 8x = -24. Then, divide both sides by 8: x = -3.

Front

What is the result of simplifying -2(3m + 9)?

Back

Using the distributive property, -2(3m + 9) simplifies to -6m - 18.

Front

What is a common mistake when solving equations like 19 - 2k = 3k - 1?

Back

A common mistake is incorrectly adding terms instead of subtracting them. In this case, you should subtract 3k from both sides.

Front

How do you find the value of k in the equation 19 - 2k = 3k - 1?

Back

First, isolate k by moving all k terms to one side and constant terms to the other side. The correct steps are: 19 + 1 = 3k + 2k, leading to k = -20.

Front

What is the result of simplifying the expression -4(8 - c) - (3c + 7)?

Back

First, apply the distributive property: -4 * 8 + 4c - 3c - 7 = -32 + c - 7 = c - 39.

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 importance of checking your work after solving an equation?

Back

Checking your work helps ensure that the solution is correct and that no mistakes were made during the solving process.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form ax + b = c, where a, b, and c are constants.