Question

4)6-5y>3y-2 5)3-7y>5y-3 6)x/6+1/2>x-1/3

Answer 1

Ответ:

Пошаговое объяснение:

4)6-5y>3y-2

-3у-5у>-6-2

3у+5у<6+2

8у<8

у<8:8

у<1

у∈(-∞;1)

5)3-7y>5y-3

-7у-5у>-3-3

7у+5у<3+3

12у<6

у<6/12

у<1/2

у∈(-∞;1/2)

6)x/6+1/2>x-1/3 |*6

х+3>6х-2

х-6х>-2-3

-5х>-5 |÷(-5)

х<1

у∈(-∞;1)

Answer 2

Let's solve each inequality step-by-step:

4. 6 - 5y > 3y - 2

To solve this inequality, we need to isolate the variable y on one side of the inequality sign. Let's do that:

Add 5y to both sides: 6 - 5y + 5y > 3y - 2 + 5y

Simplify: 6 > 8y - 2

Now, add 2 to both sides: 6 + 2 > 8y - 2 + 2

Simplify: 8 > 8y

Finally, divide both sides by 8 (since the coefficient of y is 8): 8/8 > 8y/8

Simplify: 1 > y

So the solution to the inequality is: y < 1.

5. 3 - 7y > 5y - 3

Let's solve this inequality step-by-step:

Add 7y to both sides: 3 - 7y + 7y > 5y - 3 + 7y

Simplify: 3 > 12y - 3

Now, add 3 to both sides: 3 + 3 > 12y - 3 + 3

Simplify: 6 > 12y

Finally, divide both sides by 12: 6/12 > 12y/12

Simplify: 1/2 > y

So the solution to the inequality is: y < 1/2.

6. x/6 + 1/2 > x - 1/3

Let's solve this inequality step-by-step:

To get rid of the fractions, we'll multiply the entire inequality by the least common multiple (LCM) of 6 and 2, which is 6:

6 * (x/6) + 6 * (1/2) > 6 * (x) - 6 * (1/3)

Simplify: x + 3 > 6x - 2

Now, subtract x from both sides: x + 3 - x > 6x - 2 - x

Simplify: 3 > 5x - 2

Now, add 2 to both sides: 3 + 2 > 5x - 2 + 2

Simplify: 5 > 5x

Finally, divide both sides by 5: 5/5 > 5x/5

Simplify: 1 > x

So the solution to the inequality is: x < 1.

Note: When solving inequalities, always be mindful of multiplying or dividing by a negative number, as it would reverse the inequality sign. Since we did not encounter such a situation in these examples, the direction of the inequality signs remains the same.