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Sagot :
To detect the error you have to solve the inequality, without watching the steps, and then compare them to see where Student A made the mistake.
The expression is
[tex]-2(x+4)\leq-3x[/tex]1) First step is to use the distributive property of multiplication to solve the term in parentheses
[tex]\begin{gathered} -2\cdot x+(-2)\cdot4\leq-3x \\ -2x-8\leq-3x \end{gathered}[/tex]2) Second step is to pass "-2x" to the other side of the inequation by performing the inverse operation to both sides of it:
[tex]\begin{gathered} -2x+2x-8\leq-3x+2x \\ -8\leq-x \end{gathered}[/tex]3) The term "-x" has a hidden coefficient "-1", to determine the value of "x" you'll have to divide both sides of the expression by "-1"
When working with inequalities, when you divide by a negative value, the direction gets inversed. So that:
[tex]\begin{gathered} -\frac{8}{-1}\ge-\frac{x}{-1} \\ 8\ge x \end{gathered}[/tex]If the original direction is "<" when you divide by a negative value it gets inversed to ">"
The mistake the student made was in the last step, where the student divided by a negative value but did not change the direction of the inequality.
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