Solve inequalities with negative coefficients.
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In the chart below, one equation and three inequalities are shown. For each one, write the solution and use the space in the last row to check your solution.
Inequality/Equation | $$3x = 12$$ | $$3x < 12 $$ | $$3x < - 12 $$ | $$- 3x < 12$$ |
Solution | ||||
Check solution |
What challenges arise with the inequality $${-3x<12}$$? Is this what you expected to happen?
Ralph is trying to solve the inequality $${-{ 1\over 3}(x-48)\leq15.}$$ He knows how to solve equations, so he writes the corresponding equation $${-{ 1\over 3}(x-48)=15.}$$
Rakiah is solving the inequality -$${2x+5>1.}$$ She is unsure how to treat the negative 2 in the inequality, so she uses the addition property of equality to rewrite her inequality. See her work below.
Is Rakiah’s solution correct? Justify your answer.
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Match each inequality to one of the solutions. Justify that your solution is correctly matched to your inequality.
Inequalities:
$${-10-6x>26}$$ $${-10+6x>-46}$$
Solutions:
$${x>-6 }$$ $${x>6}$$ $${ x<-6}$$ $${x<6}$$
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