Question

Negative five times a number, x, decreased by the product of two and the quantity of x increased by three is less than or equal to four decreased by triple the number, x. Which of these represents the inequality needed to solve the for the number and its solution? A. The inequality is −5x−2x+3≤4−3x and its solution is x≥−14 . B. The inequality is −5x−2(x+3)≤4−3x and its solution is x≥−52 . C. The inequality is −5x−2x+3≤4−3x and its solution is x≤−14 . D. The inequality is −5x−2(x+3)≤4−3x and its solution is x≤−52

Answer 1

Left Side

if x = a number

five times a number means 5 · a number = 5 · x

add a negative sign; -5·x

simplify; you don't need the multiplication symbol; -5x

minus 2·x = -2x

plus 3 = +3

-5n-2x+3

Sign

less than or equal to = ≤

Right Side

triple of x = 3·x = 3x

4 minus triple of x = 4-3x

4-3x

The final inequality is -5x-2x+3 ≤ 4-3x

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