Now that we have a good understanding of what equations are, let's dive into the process of solving them. Solving equations is a crucial skill in algebra as it allows us to find the value of the unknown variable.

When solving an equation, our main goal is to isolate the variable on one side of the equation. This means that we want to find the value of the variable that makes the equation true.

There are several steps involved in solving equations. The first step is to simplify both sides of the equation by combining like terms and using the properties of equality. This helps us reduce the equation to its simplest form.

Next, we aim to get the variable term on one side of the equation. We achieve this by performing inverse operations. For example, if the variable is being multiplied by a number, we can divide both sides of the equation by that number to isolate the variable.

Remember, when performing operations on an equation, it's essential to maintain the balance by applying the same operation to both sides. This ensures that the equation remains true.

In algebra, solving equations is a fundamental skill that allows us to find the value of unknown variables. Today, we will focus on one-step equations involving addition and subtraction.

When solving one-step equations, our goal is to isolate the variable on one side of the equation. To do this, we use inverse operations to undo the operations that are currently affecting the variable.

Let's start with an example:

Example 1:

Given the equation: x + 5 = 12

To solve this equation, we want to get x alone on one side. Since x is being added to 5, we need to subtract 5 from both sides to isolate x.

x + 5 - 5 = 12 - 5

x = 7

Therefore, the solution to the equation x + 5 = 12 is x = 7.

Now, let's try another example involving subtraction.

Example 2:

Given the equation: y - 3 = 8

To solve for y, we need to undo the subtraction of 3 by adding 3 to both sides of the equation.

y - 3 + 3 = 8 + 3

y = 11

Therefore, the solution to the equation y - 3 = 8 is y = 11.

Remember, when solving one-step equations involving addition and subtraction, always perform the inverse operation to isolate the variable and find the solution.

In algebra, solving equations involves performing operations to isolate the variable on one side of the equation. When dealing with one-step equations involving multiplication and division, the process is straightforward.

For one-step equations involving multiplication, the goal is to isolate the variable by performing the inverse operation. To solve for the variable, divide both sides of the equation by the coefficient of the variable. This will cancel out the multiplication and leave you with the variable on one side and the solution on the other.

Let's look at an example:

Example: Solve for x in the equation 3x = 15.

To isolate x, we need to perform the inverse operation of multiplication, which is division. Divide both sides by 3:

3x ÷ 3 = 15 ÷ 3

x = 5

Therefore, the solution to the equation 3x = 15 is x = 5.

When dealing with one-step equations involving division, the process is similar. The goal is to isolate the variable by performing the inverse operation of division, which is multiplication. To solve for the variable, multiply both sides of the equation by the divisor.

Let's consider another example:

Example: Solve for y in the equation y ÷ 4 = 6.

To isolate y, we need to perform the inverse operation of division, which is multiplication. Multiply both sides by 4:

y ÷ 4 x 4 = 6 x 4

y = 24

Therefore, the solution to the equation y ÷ 4 = 6 is y = 24.

Now, let's delve into two-step equations by combining operations. Two-step equations involve two different operations that need to be performed in order to solve for the variable. The key to successfully solving these equations is to isolate the variable by undoing the operations in reverse order. Let's look at an example:

Example: Solve for x in the equation 3x + 2 = 11.

1. Start by isolating the variable term. In this case, we have a term with a coefficient of 3 attached to x and a constant term of 2. To isolate the x, we need to undo the addition first. Since 2 is added to 3x, we will subtract 2 from both sides of the equation.

2. Subtract 2 from both sides: 3x + 2 - 2 = 11 - 2.

3. Simplify the equation: 3x = 9.

4. Next, to isolate x, we need to undo the multiplication by 3. Since 3 is multiplied by x, we will divide by 3 on both sides of the equation.

5. Divide by 3 on both sides: 3x / 3 = 9 / 3.

6. Solve the equation: x = 3.

Therefore, the solution to the equation 3x + 2 = 11 is x = 3. By following these steps and performing the inverse operation, you can successfully solve two-step equations by combining operations. Practice more examples to enhance your understanding of this concept.

Let's practice solving equations to reinforce your understanding of this important algebraic concept. Below are some practice problems for you to work on. Remember to follow the steps we discussed in the lesson:

1. Solve for x: 2x + 5 = 17

2. Solve for y: 3(y - 4) = 15

3. Solve for z: 4z/2 = 6

4. Solve for t: 5t + 10 = 35

5. Solve for a: 2(3a - 1) = 16

Now it's time for your homework assignment. Please complete the following problems and bring your work to class for discussion:

1. Solve for x: 3x - 7 = 14

2. Solve for y: 2y + 8 = 20

3. Solve for z: 6z/3 = 9

4. Solve for t: 4t - 3 = 17

5. Solve for a: 5(2a + 3) = 35

Remember to show all your steps and check your answers by substituting them back into the original equations. Good luck with your practice and homework!