Solving one- and two-step equations

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# Solving one- and two-step equations - PowerPoint PPT Presentation

Solving one- and two-step equations. Solving One-Step Equations using Additive Inverse. Steps. Equations. X + 4 = 9 -4 -4 x = 5 x – 7 = 5 +7 +7 x = 12.

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### Solving one- and two-step equations

Solving One-Step Equations using Additive Inverse

Steps

Equations

X + 4 = 9

-4 -4

x = 5

x – 7 = 5

+7 +7

x = 12

• 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)
Solving One-Step Equations using the Multiplicative Inverse

Steps

Equations

3x = 9

3x/3 = 9/3

x = 3

x /7 = 5

x/7(7) = 5(7)

x = 35

• 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)
Solving Two-Step Equations

Steps

Equations

7x + 5 = 26

-5 -5Step 1

7 x = 21

7x/7 = 21/7 Step 2

x = 3

Given the equation 7x + 5 = 26

• use the inverse of adding 5 to both sides of the equation to isolate the x.
• Use the inverse of multiplying by 7 on both sides.
Solving Two-Step Equations

Steps

Equations

x/12 - 5 = -1

+5 +5Step 1

x/12 = 4

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

x = 48

Given the equation x/12- 5 = -1

• use the inverse of subtracting 5 to both sides of the equation to isolate the x.
• Use the inverse of dividing by 12 on both sides.
Solving Equations with the variable on both sides

Steps

Equation

4x + 10 = 2x +20

-2x -2xStep 1

2x + 10 = 20

-10 -10 Step 2

2x = 10

2x/2 = 10/2 Step 3

X = 5

Given the equation

4x + 10 = 2x + 20

• Subtract 2x from both sides to get the terms with x on one side of the equation.
• Subtract 10 from both sides to get numerical terms on the other side.
• Divide both sides by 2.

Steps

Equation

X + 4 = 9

-4 -4

x = 5

Check:

X + 4 = 9

5 + 4 = 9

• You can check your solution by substituting the value back into your original equation.

Steps

Equation

7x + 5 = 26

-5 -5Step 1

7 x = 21

7x/7 = 21/7 Step 2

x = 3

Check:

7x + 5 = 26

7(3) + 5 = 26

• You can check your solution by substituting the value back into your original equation.

Steps

Equation

4x + 10 = 2x +20

-2x -2xStep 1

2x + 10 = 20

-10 -10 Step 2

2x = 10

2x/2 = 10/2 Step 3

X = 5

Check:

4x + 10 = 2x +20

4(5) + 10 = 2(5) + 20

20 + 10 = 10 + 20

30 = 30

• You can check your solution by substituting the value back into your original equation.

### Ticket out the Door

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