Question 1131538
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{{{-3(x+2) <= 5x+7}}} Given inequality


{{{-3(x)-3(2) <= 5x+7}}} Distribute


{{{-3x-6 <= 5x+7}}} Multiply


{{{-3x-6+3x <= 5x+7+3x}}} Add 3x to both sides


{{{-6 <= 8x+7}}} Combine like terms


{{{-6-7 <= 8x+7-7}}} Subtract 7 from both sides


{{{-13 <= 8x}}} Combine like terms


{{{8x >= -13}}} Flip the sides of the inequality


{{{8x/8 >= -13/8}}} Divide both sides by 8 to isolate x


{{{x >= -13/8}}} Simplify


The answer is the set of all x values such that x is equal to -13/8 or it is larger than this value


We write that answer in set-builder notation like so


*[Tex \LARGE \left\{x|x\in\mathbb{R}, \ x \ge -\frac{13}{8}\right\}]


note: The fancy R means "the set of real numbers". So saying *[Tex \Large x\in\mathbb{R}] means x is in the set of real numbers
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