Practice Solving Equations – Secure Grade 4/5 | IGCSE & GCSE Maths

Summary

In this video, Mr. Wri guides viewers through 10 exam-style math questions focused on solving equations, offering clear, step-by-step explanations. He demonstrates techniques such as expanding brackets, moving terms across the equals sign, multiplying to remove fractions, and isolating unknowns to find solutions. The tutorial covers a range of equation types, from simple linear equations to ones with variables on both sides, emphasizing strategies like identifying the side with fewer unknowns. Designed for IGCSE maths students, the video allows viewers to either follow along while solving questions or review worked solutions after attempting them, making it an interactive and practical learning resource.

Takeaways

• 😀 The video is a tutorial by Mr. Wri focused on solving algebraic equations for exam practice.
• 😀 Viewers are encouraged to download the practice questions and either work along while watching or after the video.
• 😀 The 'float and ping' method is repeatedly used to move terms with fewer unknowns across the equal sign.
• 😀 Brackets should be expanded first before performing other operations to simplify equations.
• 😀 For equations with unknowns on both sides, always move the term with the smaller coefficient to the other side.
• 😀 Multiplying both sides of a fraction equation is necessary to eliminate the denominator before solving.
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• 😀 Step-by-step calculations and use of a calculator are demonstrated for both simple and complex equations.
• 😀 Common sense approaches can sometimes quickly solve simpler equations without formal steps.
• 😀 Escalating (dividing or multiplying) is used to isolate the variable after moving terms appropriately.
• 😀 The video covers a variety of equation types, including single-step, multi-step, fractions, and negative numbers.
• 😀 Each solution is clearly worked out and explained to help students prepare for IGCSE-level maths.
• 😀 Viewers are encouraged to ask questions and comment to clarify doubts or engage further with the tutorial.

Q & A

What is the first step in solving the equation 3(2 - 4x) = 5 - 8x?

The first step is to multiply out the bracket on the left-hand side: 3 * 2 gives 6, and 3 * -4x gives -12x, resulting in 6 - 12x = 5 - 8x.

In the equation y = (2y + 1)/5, how do you eliminate the fraction?

Multiply both sides of the equation by 5 to eliminate the fraction: 5y = 2y + 1.

How do you determine which side of an equation to move the variable from?

You should move the variable with the smaller coefficient to the other side to simplify calculations. This is referred to in the video as 'float and ping.'

What is the solution to 8g = 40?

Divide both sides by 8 to isolate g: g = 40 / 8, so g = 5.

For the equation 19 - k = 4, how can you quickly find k?

Using simple subtraction: 19 minus what equals 4? So k = 15.

In the equation 3(2x - 5) = 9 - x/2, why do you multiply everything by 2?

Multiplying by 2 eliminates the fraction -x/2 on the right-hand side, simplifying the equation for easier calculation.

What is the method used to solve 4(x - 3) = 7x + 15?

First, expand the bracket: 4x - 12 = 7x + 15. Then move 4x to the right and constants to the left: -12 - 15 = 3x, which gives x = -9.

How do you solve p = (3p - 5)/10?

Multiply both sides by 10: 10p = 3p - 5. Then subtract 3p: 7p = -5. Finally, divide by 7: p = -5/7.

What steps are taken to solve (2x - 3)/4 = 3x - 5?

Multiply both sides by 4 to eliminate the denominator: 2x - 3 = 12x - 20. Then move 2x: -3 = 10x - 20, add 20: 17 = 10x, and divide by 10: x = 1.7.

When solving (2x + 5)/6 = 2x - 5, why is it necessary to multiply both sides by 6?

Multiplying by 6 removes the fraction on the left-hand side, resulting in 2x + 5 = 12x - 30, which simplifies the equation for easier solving.

What does the term 'float and ping' mean in the context of solving equations?

It is an informal term used in the video that means 'move a term from one side of the equation to the other,' usually to isolate the variable.

Why is it helpful to check which side has the fewest unknowns before moving terms?

Moving the smaller coefficient reduces calculation complexity and makes solving the equation easier.