Solving Equations

Front

What is the first step in solving the equation 2x - (3 + 4x) = 11?

Back

Distribute the negative sign and simplify the equation.

Front

How do you isolate the variable in the equation x = 2x - 4?

Back

Subtract 2x from both sides to get -x = -4, then multiply by -1 to find x = 4.

Front

What is the solution to the equation 12 - 4x - x = 2?

Back

Combine like terms to get -5x = -10, then divide by -5 to find x = 2.

Front

In the equation 4y - 7 = 2y + 7, how do you solve for y?

Back

Add 7 to both sides and then subtract 2y from both sides to get 2y = 14, then divide by 2 to find y = 7.

Front

What is the process to solve the equation 3x - 4(2 + 3x) = 82?

Back

Distribute -4 to both terms in the parentheses, combine like terms, and isolate x.

Front

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

Back

To manipulate 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 combining like terms when solving equations?

Back

It simplifies the equation, making it easier to isolate the variable.

Front

What is the definition of a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form ax + b = c.

Front

How do you check if your solution to an equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What is the significance of the equal sign in an equation?

Back

It indicates that the expressions on both sides have the same value.