Solving Equations

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What is the first step in solving the equation 2y + 7 = 11?

Back

Subtract 7 from both sides to isolate the term with the variable: 2y = 4.

Front

How do you isolate a variable in an equation?

Back

You can isolate a variable by performing inverse operations, such as addition, subtraction, multiplication, or division, to both sides of the equation.

Front

What is the solution to the equation 2y + 7 = 11?

Back

y = 2.

Front

What is the process to solve the equation 10x + 9 = 4x - 9?

Back

First, subtract 4x from both sides: 6x + 9 = -9. Then, subtract 9 from both sides: 6x = -18. Finally, divide by 6: x = -3.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that can satisfy the equation.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions if any value for the variable satisfies the equation, indicating that both sides are equivalent.

Front

Solve for x: 8x - 8 = -4x + 16.

Back

x = 2.

Front

What is the solution to the equation 4(1-x)+3x=-2(x+1)?

Back

x = -6.