Model and Solve One-Variable Equations with Variables on Both Sides of the Equal Sign

Mathematical Equivalence

ON

Solve the equation for the variable

In the equation 5d - 1= 2d - 7, we need to get the variable to one side of the equal sign. What would we do to move the variable to the left side?

• -2 from both sides of the equal sign

• -5d from both sides of the equal sign

• -2d from both sides of the equal sign

• + 7 on both sides of the equal sign

In the equation 5d - 1= 2d - 7, after we -2d from both sides, we get 3d - 1 = -7. What does d = if you finish solving it?

• d = -1

• d = 1

• d = 2

• d = -2

Solve:
7x - 3x - 8 = 24

• 8

• -8

• 3.2

• 4

The goal of solving equations is to:

• Find the constant

• Find the coefficient

• Isolate the Variable

• Be confused

Choose ALL of the steps in SOLVING an equation.

• Distribute

• Move all the variables to ONE side.

• Combine Like Terms

• Move ALL the CONSTANTS to the other.

• Get Rid of the Coefficient.

WRITE AN EQUATION FROM THE MODEL

• 8

• 2X+28 = 20

• X+12+16+X = 20

• -8

Choose ALL of the steps in SIMPLIFYING EACH SIDE of an equation.

• Distribute

• Move all the variables to ONE side.

• Combine Like Terms

• Move ALL the CONSTANTS to the other.

• Get Rid of the Coefficient.

Find the value of  x  in the equation modeled by the algebra tiles. Hint...write down the equation...use the key. There are variables on both sides. Solve the equation using our 5 steps...or use the L-R strategy in Desmos. Either way...check in Desmos. NOTE: Only type in a number...not the x= part.

Answer explanation

The equation modeled is

4x - 2 = 2x + 4

...solve how you will...the Desmos check verifies that x = 3.