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Find all possible values of 𝑥 given the modulus of 𝑥 plus a half is equal to three-quarters.
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We know that the modulus or absolute value of a number is its distance from zero.
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This means that we have two possible solutions: either 𝑥 plus a half is equal to three-quarters or 𝑥 plus a half is equal to negative three-quarters.
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In both of these equations, we need to subtract one-half from both sides.
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As subtracting one-half is the same as subtracting two-quarters, we have values of 𝑥 equal to one-quarter and negative five-quarters.
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The two values that satisfy the equation the absolute value or modulus of 𝑥 plus one-half is equal to three-quarters are one-quarter and negative five-quarters.