Solving Equations

Front

What is the first step in solving the equation 2(2x + 3) = -6(x + 9)?

Back

Distribute the constants on both sides of the equation.

Front

How do you isolate the variable in the equation 2(a + 4) = 2a - 8 + 4a?

Back

Combine like terms and then move all terms involving 'a' to one side.

Front

What is the process to solve the equation 7x - 3x - 8 = 24?

Back

Combine like terms (7x - 3x) and then isolate x by adding 8 to both sides.

Front

In the equation 32 - 7x = -6(x + 3), what should you do first to simplify it?

Back

Distribute -6 to both terms inside the parentheses.

Front

What is the final step to solve the equation 7x + 19 = -2x + 55?

Back

Combine like terms and isolate x by moving all x terms to one side.

Front

What does it mean to 'isolate the 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 your solution after solving an equation?

Back

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

Front

What is the role of the distributive property in solving equations?

Back

It allows you to multiply a single term by terms inside parentheses, simplifying the equation.