WEBVTT
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Find the solution set of the modulus of π₯ plus three equals the modulus of two π₯ minus six.
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Before we look at this specific question, it is worth doing a quick recap of what the modulus function means.
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If we look at the example modulus of π₯ equals four, then the answer could be positive four or negative four.
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Therefore, the solution set would contain the two values negative four and positive four.
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In order to find the solution set of modulus π₯ plus three equals modulus two π₯ minus six, weβll need to solve two equations: firstly π₯ plus three equals two π₯ minus six and secondly π₯ plus three equals the negative of two π₯ minus six in the parentheses.
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Letβs consider the left-hand equation first.
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In order to balance this equation, we can firstly add six to both sides.
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This leaves us with π₯ plus nine equals two π₯.
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Our second step would be to subtract π₯ from both sides, leaving us with nine on the left-hand side and π₯ on the right-hand side.
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Therefore, one solution is π₯ equals nine.
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Now letβs look at the right-hand equation.
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The first thing we will do here is remove the parentheses from the right-hand side.
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This leaves us with π₯ plus three equals negative two π₯ plus six.
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We then begin to balance the equation.
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Firstly, we have subtracted three from both sides.
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This leaves us with π₯ equals negative two π₯ plus three.
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Our second step is to add two π₯ to both sides, leaving us three π₯ equals three.
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Finally, we divide both sides by three, giving us another solution π₯ equals one.
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Solving these two equations gives us a solution set of one and nine.
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When we solve the equation, modulus π₯ plus three equals the modulus of two π₯ minus six.