You can write the same number of nagative tiles on each side of the equation.
Equation: - 3x + 4 = - 11 Solution: x = 5
Practice makes perfect
We are given the equation modeled by the algebra tiles.
We can see that the given equation is - 3x + 4 = - 11. To solve the equation modeled by the algebra tiles, we have to get the x-tile alone on one side of the equation. We know that a positive tile and a negative tile will cancel each other out.
We will remove the four positive tiles that are on the same side of the equation as the three negative x-tiles. From the Subtraction Property of Equality, we know that we can write the same number of negative tiles on both sides of the equation and the new equation will be equivalent. Let's do it!
Next, let's rewrite the equation a little by pairing as many negative and positive tiles together as we can on both sides.
A pair of negative and positive tiles is equal to 0. This means that we can remove each matched pair. Let's do it!
Next, we will take the negative x-tiles and divide them into three groups so that each negative x-tile is alone. We will do the same with the right-hand side of the equation.
We obtained three equations that are the same. We can remove two of them.
We are left with the isolated negative x-tile on the left-hand side of the equation and five negative tiles on the right-hand side. If negative tiles are equal, then the positive tiles are also equal.
We found that the solution is x = 5. We will check our answer using properties of equality. Let's consider the given equation.
- 3x + 4 = - 11
First, we will use the Subtraction Property of Equality.
Subtraction Property of Equality
Subtracting the same number from each side of an equation produces an equivalent equation.
Let's use this property and subtract 4 from both sides of the equation.
