Equivalent Equations

Front

What is an equivalent equation?

Back

An equivalent equation is an equation that has the same solution as another equation. For example, if 2x + 6 = -3, then 4x + 12 = -6 is an equivalent equation.

Front

If 2x + 6 = -3, what is the value of x?

Back

x = -rac{9}{2} or -4.5.

Front

If 4x = 6, what is the value of x?

Back

x = rac{3}{2} or 1.5.

Front

If 3x - 2 = 5, what is the value of x?

Back

x = rac{7}{3} or approximately 2.33.

Front

What is the relationship between the coefficients in equivalent equations?

Back

The coefficients of the variables in equivalent equations maintain a consistent ratio.

Front

If 2x + 6 = -3, what is the value of 4x + 12?

Back

4x + 12 = -6.

Front

If 4x = 6, what is the value of 2x?

Back

2x = 3.

Front

If 3x - 2 = 5, what is the value of 9x - 6?

Back

9x - 6 = 15.

Front

What is the principle of maintaining equality in equations?

Back

To maintain equality, whatever operation is performed on one side of the equation must also be performed on the other side.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable alone on one side of the equation.