Question

Solve the inequalities please

Answer 1

#1

• 3x+12-6x≤-9
• -3x+12≤-9
• -3x≤-21
• 3x≥21
• x≥7

#2

• x+5x-6<12
• 6x<18
• x<3

#3

• 5(x+8)-7≤23
• 5x+40≤30
• 5x≤-10
• x≤-2

#4

• 4x-6≥6x-20
• -2x≥-14
• x≤7

Answer 2

`\huge\text{Answer:}`

Inequality number 1: x≥7

Inequality number 2: x<3

Inequality number 3: x≤-2

Inequality number 4: x≤7

`\huge\text{Solution:}`

1. 3x+12-6x≤-9

3x-6x+12≤-9

Subtract the x's:

-3x+12≤-9

-3x≤-9-12

-3x≤-21

3x≥21

x≥7

2. x+5x-6<12

6x-6<12

Move 6 to the right, using the
`\bold{\underline{opposite ~operation}}`:

6x<12+6

6x<18

Now, divide both sides by 6:

x<3

3. 5(x+8)-7≤23

Use the Distributive Property:

5x+40-7≤23

5x+33≤23

5x≤23-33

5x≤-10

x≤-2

4. 4x-6≥6x-20

4x-6x≥-20+6

-2x≥-14

2x≤14

x≤7

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Note:

If we divide both sides of the inequality by a negative variable, we flip the inequality sign.

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Hope you find it helpful.

Feel free to ask if you have any doubts.