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Subtracting 16 from each side gives -5a (negative 5 times a) = -3 (negative 3). We can think of this as 16 has been added to a, after it has been multiplied by -5 (negative 5).
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Here’s another example: Solve 16 – 5a = 13.
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Subtracting 7 from each side will give 5p = 30, and then dividing both sides by 7 will give p = 6. The correct inverse operations will be to subtract 7 and then divide by 5. For example, the expression 5p + 7, means that p has been multiplied by 5 and then 7 has been added. More than one operation may have been applied to form the equation. So, we have to be able to work out the order in which the operations were applied to the variable (or letter). Step 3 - Decide on the Order of Operations So, after dividing both sides by 5, we have that p = 6, and as we know what value of p makes the equation equal, we have solved the equation. The left-hand side of the equation won’t equal the right-hand side if you only divide one side by 5. For an equation to retain the property of being equal on each side, you must do the same thing to each side. It’s helpful to think of the equation as sitting on a balance scale.
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For example, if you want to reverse the effect of adding 5 to both sides of an equation, you should subtract 5 from each side. In formal mathematical terms, you applied the inverse operation to multiplying by 5 to both sides of the equation to find the answer: 6.īelow is a table that shows the inverse operation for each operation. You both may have counted through your 5 times table until you got to 30 and realised that the number in the box was 6. Your child will understand that a variable, in its simplest form here, is just the letter that they need to find the value of, in order to solve the equation.Īs we need to undo or reversethe operations that have been applied to our variable to give the value stated in the equation, your child needs to understand the inverse of multiplying, dividing, adding and subtracting.Īsk your child to think about how they would fill in the number missing from the box in the puzzle below: For example, 6x + 7y - 3.Ī term is an individual number or a value (much like a word in a sentence). You could consider an expression to be the equivalent of a phrase made up of words – it consists of terms and their operators. For example, if bread rolls come in packets of 6, how many packets do you need to buy to have 24 buns? Or, if a special offer means you can buy 3 chocolate bars for £3.60, is this cheaper than buying them singularly at £1.30 each? However, can your child solve the following equation and demonstrate each step of their working? 6y - 21 = 63Įvery good lesson has a purpose or an objective. We're confident that if you follow the step-by-step approach below your child will be able to:ġ) Understand how to solve two-step equationsĢ) Apply this understanding to practice questionsīefore we jump into solving equations it’s important to check that your child understands some key terminology.Īn equation is simply a statement that tells us what an expression equals for one (or more values) of the variable in the equation. Number puzzles pop up frequently in everyday life so we’re used to solving them.