Flashcards · Maths · Algebra
Solving Linear Equations and Inequalities
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What is the golden rule of solving equations?
Do the same thing to both sides.
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How do you solve \(3x - 4 = 11\)?
Add 4 to get \(3x = 15\), then divide by 3: \(x = 5\).
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How do you solve \(5 - 2x = 11\)?
Subtract 5 to get \(-2x = 6\), then divide by \(-2\): \(x = -3\).
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What is the first step when there are unknowns on both sides?
Collect the \(x\) terms on one side by subtracting the smaller \(x\) term from both sides.
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Solve \(5x + 3 = 2x + 18\).
\(3x = 15\), so \(x = 5\).
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Solve \(3(2x - 1) = 4x + 9\).
Expand to \(6x - 3 = 4x + 9\), so \(2x = 12\) and \(x = 6\).
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How do you solve \(\dfrac{x + 5}{3} = \dfrac{x - 1}{2}\)?
Multiply both sides by 6 to get \(2(x + 5) = 3(x - 1)\), which gives \(x = 13\).
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What is the first step in forming an equation from a problem?
Say what the letter stands for, then write the other quantities in terms of it.
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How do you write three consecutive integers?
\(n\), \(n + 1\) and \(n + 2\), which add up to \(3n + 3\).
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What do the angles in a triangle add up to?
\(180^\circ\), so an angle equation is set equal to 180.
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What do the symbols \(<\), \(>\), \(\leq\) and \(\geq\) mean?
Less than, greater than, less than or equal to, and greater than or equal to.
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What is the special rule for inequalities?
Reverse the inequality sign when you multiply or divide both sides by a negative number.
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Solve \(-2x > 6\).
\(x < -3\). The sign reverses when you divide by \(-2\).
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What do an open circle and a filled circle mean on a number line?
An open circle means the value is not included (\(<\) or \(>\)). A filled circle means it is included (\(\leq\) or \(\geq\)).
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Which integers satisfy \(-2 \leq x < 4\)?
\(-2, -1, 0, 1, 2, 3\). The value \(-2\) is included and 4 is not.
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How do you write ‘at most 20’ as an inequality?
\(x \leq 20\).
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How can you check the solution to an equation?
Substitute it back into the original equation and see whether both sides match.