Solving Equations

Front

What is the first step to solve the equation -2(x + 5) = -30?

Back

Distribute -2 to both terms inside the parentheses: -2x - 10 = -30.

Front

How do you isolate the variable x in the equation 5(x - 3) + 2x = 27?

Back

Combine like terms: 5x - 15 + 2x = 27, then add 15 to both sides: 7x = 42, and finally divide by 7: x = 6.

Front

What is the solution to the equation 3x - 5 = 5x + 11?

Back

Rearranging gives -2x = 16, so x = -8.

Front

How do you solve the equation 2x - 3 = -9?

Back

Add 3 to both sides: 2x = -6, then divide by 2: x = -3.

Front

What is the value of x in the equation 52 = -8 + 10x?

Back

Add 8 to both sides: 60 = 10x, then divide by 10: x = 6.

Front

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

Back

To isolate a variable means to manipulate the equation so that the variable is on one side and all other terms are on the other side.

Front

What is the principle of balancing equations?

Back

Whatever you do to one side of the equation, you must do to the other side to maintain equality.

Front

What is a linear equation?

Back

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

Front

What is the solution set of an equation?

Back

The solution set is the set of all values that satisfy the equation.

Front

What is the distributive property?

Back

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