13. The sum of six times a number and five is greater than the difference of three times a number and two. 14. The difference of twenty-seven and five times a number is less than or equal to four times a number.

Question

13. The sum of six times a number and five is greater than the difference of three times a number and two. 14. The difference of twenty-seven and five times a number is less than or equal to four times a number.

Answer 1

13. Let's denote the unknown number as x. According to the given information, we can write the inequality as:6x + 5 > 3x - 2To solve this inequality, we need to isolate x. First, let's subtract 3x from both sides:6x - 3x + 5 > 3x - 3x - 2This simplifies to:3x + 5 > -2Next, let's subtract 5 from both sides:3x + 5 - 5 > -2 - 5This simplifies to:3x > -7Finally, let's divide both sides by 3:3x/3 > -7/3This simplifies to:x > -7/3So, the solution to the inequality is x > -7/3.14. Let's denote the unknown number as y. According to the given information, we can write the inequality as:27 - 5y ≤ 4yTo solve this inequality, we need to isolate y. First, let's add 5y to both sides:27 - 5y + 5y ≤ 4y + 5yThis simplifies to:27 ≤ 9yNext, let's divide both sides by 9:27/9 ≤ 9y/9This simplifies to:3 ≤ ySo, the solution to the inequality is y ≥ 3.

Problemas

13. The sum of six times a number and five is greater than the difference of three times a number and two. 14. The difference of twenty-seven and five times a number is less than or equal to four times a number.

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