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Maths-

SAT

Easy

Question

If $y equals x plus 1 half$ and z = 2x −3, which of the following is equivalent to y + yz ?

2x² - x - 1
2x² - x - 2
$2 x^{2} - x - \frac{1}{2}$
$2 x^{2} - 2 x - \frac{3}{2}$

The correct answer is: 2x² - x - 1

$y equals x plus 1 half & space z equals 2 x minus 3$
$y plus y z equals y left parenthesis 1 plus z right parenthesis equals open parentheses x plus 1 half close parentheses left parenthesis 1 plus 2 x minus 3 right parenthesis$
$equals open parentheses x plus 1 half close parentheses left parenthesis 2 x minus 2 right parenthesis equals 2 open parentheses x plus 1 half close parentheses left parenthesis x minus 1 right parenthesis$
= (2x+1)(x - 1) = 2x² + x - 2x -1
= 2x² - x - 1.

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