How to solve one-step equations | Linear equations | Algebra I | Khan Academy

Summary

This educational transcript explains the process of solving equations by maintaining equality. It uses the example of 'x + 7 = 10' to demonstrate how subtracting 7 from both sides isolates 'x' and results in 'x = 3'. The concept is further illustrated with '-a - 5 = -2', showing that adding 5 to both sides eliminates the '-5' and yields 'a = 3'. The summary emphasizes the importance of treating both sides of the equation equally to preserve balance, making it easier to solve for the unknown variable.

Takeaways

• 🔍 The script explains the process of solving equations by maintaining equality on both sides.
• 📘 The first example involves solving for 'x' in the equation 'x + 7 = 10'.
• ➖ To isolate 'x', seven is subtracted from both sides of the equation.
• 🔢 The subtraction results in 'x = 10 - 7', which simplifies to 'x = 3'.
• 🔄 The concept of balance is used, likening the equation to a scale that must remain level.
• 🔎 The script emphasizes that any operation performed on one side of the equation must be mirrored on the other side.
• 📝 A verification step is suggested to ensure the solution is correct, such as checking if '3 + 7' equals '10'.
• 🔁 The second example provided is 'a - 5 = -2', which also involves negative numbers.
• ➕ To solve for 'a', five is added to both sides to cancel out the '-5' on the left side.
• 📉 The addition leads to 'a = -2 + 5', which simplifies to 'a = 3'.
• 🔍 The script demonstrates that the same principles apply regardless of the presence of negative numbers.

Q & A

What is the purpose of the script?

The purpose of the script is to explain the process of solving equations by maintaining the balance of both sides, using the concept of adding or subtracting the same value from both sides to isolate the unknown variable.

What is the first equation presented in the script?

The first equation presented is x + 7 = 10.

How does the script suggest solving for x in the equation x + 7 = 10?

The script suggests subtracting 7 from both sides of the equation to isolate x, resulting in x = 10 - 7, which simplifies to x = 3.

What is the verification step mentioned for the equation x + 7 = 10?

The verification step is to check if the solution (x = 3) is correct by adding 7 to it, ensuring that 3 + 7 equals 10.

What is the second equation discussed in the script?

The second equation discussed is a - 5 = -2.

How is the equation a - 5 = -2 approached to solve for a?

The script suggests adding 5 to both sides of the equation to cancel out the -5 on the left side, resulting in a = -2 + 5, which simplifies to a = 3.

What is the verification step for the equation a - 5 = -2?

The verification step is to check if the solution (a = 3) is correct by subtracting 5 from it, ensuring that 3 - 5 equals -2.

What is the key principle used in both examples to solve for the unknown variable?

The key principle used is maintaining equality by performing the same operation on both sides of the equation, which ensures the balance is kept like a scale.

Why is it important to perform the same operation on both sides of the equation?

Performing the same operation on both sides is important to maintain the equality, ensuring that the solution found for the unknown variable is correct.

Can the method demonstrated in the script be applied to more complex equations?

Yes, the method can be applied to more complex equations, as long as the same principles of maintaining equality by performing the same operations on both sides are followed.

What is the significance of the 'scales' analogy used in the script?

The 'scales' analogy is used to illustrate the need for balance in an equation, emphasizing that any operation performed on one side must be mirrored on the other to keep the equation valid.