Solving 1-Step Equations

• Math
• 7th Grade

Solving Equations

Solving 1- Step

 Equations

11/4/24

Objectives:

-Understand the process to solving 1-Step equations.

- Identify the operation neccessary to solve 1-step equations. 

-Solve 1-step equations.

Addition and Subtraction

If you are moving a positive number to the other side of the equal sign, then you will use subtraction.

If you are moving a negative number to the other side of the equal sign, then you will use addition.

$$x+2=0$$

$$3+x=1$$

$$2=x+5$$

$$4=1+x$$

Examples:

Examples:

$$x-5=0$$

$$-2+x=3$$

$$-1=-4+x$$

$$2=x-6$$

First, you have to identify which operation you will need to use to get      by itself.

$$x$$

Addition and Subtraction

Second, use the identified operation to add or subtract the value to both sides of the equation.

Examples:

$$x+2=0$$

$$-2$$

$$-2$$

$$x-5=0$$

$$+5$$

$$+5$$

$$2=x+5$$

$$4=1+x$$

$$3+x=1$$

$$-2+x=3$$

$$2=x-6$$

$$-1=-4+x$$

$$-5$$

$$-5$$

$$-1$$

$$-1$$

$$-3$$

$$-3$$

$$+6$$

$$+6$$

$$+2$$

$$+2$$

$$+4$$

$$+4$$

Addition and Subtraction

Third, carry out the appropriate operation to solve for    . 

Examples:

$$x+2=0$$

$$-2$$

$$-2$$

$$x-5=0$$

$$+5$$

$$+5$$

$$2=x+5$$

$$4=1+x$$

$$3+x=1$$

$$-2+x=3$$

$$2=x-6$$

$$-1=-4+x$$

$$-5$$

$$-5$$

$$-1$$

$$-1$$

$$-3$$

$$-3$$

$$+6$$

$$+6$$

$$+2$$

$$+2$$

$$+4$$

$$+4$$

$$x$$

$$x=-2$$

$$x=3$$

$$x=-3$$

$$x=-2$$

$$x=5$$

$$x=5$$

$$x=8$$

$$x=3$$

Identify the operation needed to solve for     .

$$x$$

<span style="color: rgb(15, 25, 102)">Addition</span>

<span style="color: rgb(15, 25, 102)">Subtraction</span>

x + 2 = 5

x - 3 = 4

-3 + x = 6

4 + x = 3

2 = x - 3

0 = -5 + x

1 = 4 + x

6 = x + 4

Division and Multiplication

If      is being multiplied by a number, then you will use division.

If      is being divided by a number, then you will use multiplication.

Examples:

Examples:

First, you have to identify which operation you will need to use to get      by itself.

$$x$$

$$x$$

$$x$$

$$3x=0$$

$$-2x=4$$

$$1=2x$$

$$3=-6x$$

$$\frac{x}{2}=0$$

$$\frac{x}{-3}=2$$

$$1=\frac{x}{4}$$

$$2=\frac{x}{-5}$$

Division and Multiplication

Examples:

Second, use the identified operation to divide or multiply both sides of the equation by the value.

$$\frac{3x}{3}=\frac{0}{3}$$

$$\frac{-2x}{-2}=\frac{4}{-2}$$

$$\frac{1}{2}=\frac{2x}{2}$$

$$\frac{3}{-6}=\frac{-6x}{-6}$$

$$\frac{x}{2}\cdot 2=0\cdot 2$$

$$\frac{x}{-3}\cdot -3=2\cdot -3$$

$$1\cdot 4=\frac{x}{4}\cdot 4$$

$$2\cdot -5=\frac{x}{-5}\cdot -5$$

Division and Multiplication

Examples:

Third, carry out the appropriate operation to solve for    .

$$\frac{3x}{3}=\frac{0}{3}$$

$$\frac{-2x}{-2}=\frac{4}{-2}$$

$$\frac{1}{2}=\frac{2x}{2}$$

$$\frac{3}{-6}=\frac{-6x}{-6}$$

$$\frac{x}{2}\cdot 2=0\cdot 2$$

$$\frac{x}{-3}\cdot -3=2\cdot -3$$

$$1\cdot 4=\frac{x}{4}\cdot 4$$

$$2\cdot -5=\frac{x}{-5}\cdot -5$$

$$x$$

$$x=0$$

$$x=-2$$

$$x=\frac{1}{2}$$

$$x=-\frac{1}{2}$$

$$x=0$$

$$x=4$$

$$x=-6$$

$$x=-10$$

Identify the operation needed to solve for     .

$$x$$

<span style="color: rgb(15, 25, 102)">Division</span>

<span style="color: rgb(15, 25, 102)">Multiplication</span>

x/3 = 4

4x = 4

x/2 = -6

-3x = 5

2 = 6x

0 = x/-5

1 = -4x

6 = x/4

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