Solving one- and two-step equations

Solving One-Step Equations using Additive Inverse

Steps• Given the equation x + 4 = 9

use the inverse of adding 4 to both sides of the equation to isolate the x. (In other words, subtract 4 from each side to get x by itself.)

• Given the equation x – 7 = 5 use the inverse of subtracting 7 to both sides. (In other words, add 7 to both sides)

Equations• X + 4 = 9 -4 -4 x = 5

• x – 7 = 5 +7 +7 x = 12

Solving One-Step Equations using the Multiplicative Inverse

Steps• Given the equation 3x +4 =

9 use the inverse of multiplying 3 to both sides of the equation to isolate the x. (In other words, divide 3 from each side to get x by itself.)

• Given the equation x /7 = 5 use the inverse of dividing by 7 to both sides. (In other words, multipy both sides by 7)

Equations• 3x = 9 3x/3 = 9/3 x = 3

• x /7 = 5x/7(7) = 5(7) x = 35

Solving Two-Step Equations

StepsGiven the equation 7x + 5 = 26 1. use the inverse of adding 5

to both sides of the equation to isolate the x.

2. Use the inverse of multiplying by 7 on both sides.

Equations

• 7x + 5 = 26 -5 -5 Step 1 7 x = 21 7x/7 = 21/7 Step 2 x = 3

Solving Two-Step Equations

StepsGiven the equation x/12- 5 = -1 1. use the inverse of

subtracting 5 to both sides of the equation to isolate the x.

2. Use the inverse of dividing by 12 on both sides.

Equations

x/12 - 5 = -1 +5 +5 Step 1

x/12 = 4 x/12(12) = 4(12) Step 2

x = 48

Solving Equations with the variable on both sides

StepsGiven the equation 4x + 10 = 2x + 201. Subtract 2x from both sides

to get the terms with x on one side of the equation.

2. Subtract 10 from both sides to get numerical terms on the other side.

3. Divide both sides by 2.

Equation4x + 10 = 2x +20-2x -2x Step

12x + 10 = 20 -10 -10 Step

2 2x = 10 2x/2 = 10/2 Step 3 X = 5

Checking your solution

Steps• You can check your solution

by substituting the value back into your original equation.

Equation X + 4 = 9 -4 -4 x = 5

Check:X + 4 = 95 + 4 = 9

Checking your solution

Steps• You can check your solution

by substituting the value back into your original equation.

Equation 7x + 5 = 26 -5 -5 Step 1 7 x = 21 7x/7 = 21/7 Step 2 x = 3

Check: 7x + 5 = 267(3) + 5 = 26

Checking your solution

Steps• You can check your solution

by substituting the value back into your original equation.

Equation 4x + 10 = 2x +20-2x -2x Step 12x + 10 = 20 -10 -10 Step 2 2x = 10 2x/2 = 10/2 Step 3 X = 5Check:4x + 10 = 2x +204(5) + 10 = 2(5) + 2020 + 10 = 10 + 2030 = 30

Ticket out the Door

What properties of addition and multiplication can I use to solve one

and two step?