Question

Practice solving one-variable equations using the distributive property. Identify the method that will be used to solve for x for each equation. 4x = 20 x – 11 = 9 5x + 6x = 22 5(x – 2) = 30

Answer 1

The methods used by the equations are Direct substitution, Isolating x using addition/subtraction, Combining like terms, and Distributing and combining like terms respectively. The values of x in every equation are 5, 20, 2, and 8 respectively.

For Equation 1: 4x = 20

The method used is Direct substitution. This equation is already solved for x. We can simply divide both sides by 4 to get x:

x = 20 / 4

x = 5

For Equation 2: x – 11 = 9

The method used is Isolating x using addition/subtraction. Add 11 to both sides to isolate x on the left side:

x – 11 + 11 = 9 + 11

x = 20

For Equation 3: 5x + 6x = 22

The method used is Combining like terms. Combine the 5x and 6x terms on the left side:

11x = 22

Then, divide both sides by 11 to solve for x:

x = 22 / 11

x = 2

For Equation 4: 5(x – 2) = 30

The method used is Distributing and combining like terms. First, use the distributive property to distribute the 5 on the left side:

5x – 10 = 30

Then, we combine the x terms on the left side:

5x – 10 + 10 = 30 + 10

5x = 40

Finally, we divide both sides by 5 to solve for x:

x = 40 / 5

x = 8