A 10 € note pays for 3 identical notebooks and leaves 1 € in change. How much does each notebook cost? Setting up $3x + 1 = 10$ is something you already know how to do from 1st ESO. This year you are going to solve slightly trickier equations: with brackets and denominators at the same time, and you will find out what happens when an equation has no solution at all or has every number as a solution.
Review: the balance
The golden rule is still the same: whatever you do to one side, you do to the other. This is where the transposition of terms you already know comes from:
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Solve these one-step equations mentally by applying the addition rule (what is added is subtracted on the other side and vice versa): a) $x + 12 = 30$ b) $x - 8 = 15$ c)…
Solve these one-step equations mentally by applying the addition rule (what is added is subtracted on the other side and vice versa):
Marta went to the stationer's and bought 3 identical notebooks. If she paid with a $10$ € note and received $1$ € change, set up an equation where $x$ is the price of…
Marta went to the stationer's and bought 3 identical notebooks. If she paid with a $10$ € note and received $1$ € change, set up an equation where $x$ is the price of one notebook and solve it to find how much each one cost.
"Real" equations often have brackets and fractions at the same time. The usual order is this (if the brackets are inside the numerators, as in the example, it is easier to clear the denominators first and then expand the brackets):
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Solve the following linear equation by correctly applying the distributive property and collecting like terms: $4(2x - 3) - 2(5 - 3x) = 3(x + 1) + 5$
Solve the following linear equation by correctly applying the distributive property and collecting like terms:
Solve the following linear equation, paying special attention to the negative signs in front of fractions and using the lowest common multiple to simplify denominators:…
Solve the following linear equation, paying special attention to the negative signs in front of fractions and using the lowest common multiple to simplify denominators:
When you simplify an equation you almost always end up with $x = \text{something}$, but there are two special cases:
In the end you get…
Example
It means
$ax = b$ with $a \neq 0$
$3x = 9$
One solution: $x = 3$
$0x = b$ with $b \neq 0$
$0x = 5$
No solution (it is never true that $0 = 5$)
$0x = 0$
$0x = 0$
Infinitely many solutions (it is an identity)
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Look at the following set of scales in balance. If all the blue boxes are identical and weigh $x$ kilograms, and the orange weights show their weight in kg, set up and…
Look at the following set of scales in balance. If all the blue boxes are identical and weigh $x$ kilograms, and the orange weights show their weight in kg, set up and solve the equation to find the value of $x$.
Many word problems translate directly into a first-degree equation: ages, sharing out quantities, moving objects that meet…
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Marcos has bought three strategy games and two battle passes in a digital store. Each battle pass costs half as much as a game. If he paid $70$ € in total, what is the…
Marcos has bought three strategy games and two battle passes in a digital store. Each battle pass costs half as much as a game. If he paid $70$ € in total, what is the price of a game and what is the price of a battle pass?