Equivalent Equations

Front

What is an equivalent equation?

Back

Front

Solve the equation: -5x = 25

Back

x = -5

Front

If you multiply both sides of an equation by the same non-zero number, what happens?

Back

The two sides remain equal, and the equation is still valid.

Front

What is the first step to solve the equation 3a + 9 + 4a = 2?

Back

Combine like terms to get 7a + 9 = 2.

Front

What is the solution to the equation 5x + 30 = 45?

Back

x = -6, because 5(x + 6) = 45 is equivalent.

Front

Identify the error in the following steps: 19 - 2k = 3k - 1; +3k; 19 + 1k = -1; -19; k = -20.

Back

Instead of adding 3k, they should subtract 3k.

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

Solve for x: 2x + 3 = 11

Back

x = 4.

Front

What is the principle of equality in equations?

Back

The principle of equality states that if two expressions are equal, you can perform the same operation on both sides without changing the equality.

Front

What is the solution to the equation 4(x - 2) = 16?

Back

x = 6.