Question

-6x+18>=0 3x-7<4.8x-1.6 4(3x-2)>6-2(5+4x)

Answer 1

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Answer 2

Let's solve each inequality step by step:

1. -6x + 18 >= 0: To solve this inequality, first, we need to isolate the variable x.

Step 1: Subtract 18 from both sides. -6x >= -18

Step 2: Divide both sides by -6, but remember to reverse the inequality when dividing by a negative number. x <= -18 / -6

Simplifying: x <= 3

So the solution to the first inequality is x <= 3.

2. 3x - 7 < 4.8x - 1.6: To solve this inequality, let's isolate the variable x.

Step 1: Subtract 3x from both sides. -7 < 4.8x - 3x - 1.6

Step 2: Combine like terms. -7 < 1.8x - 1.6

Step 3: Add 1.6 to both sides. -5.4 < 1.8x

Step 4: Divide both sides by 1.8, or multiply by 1/1.8 (which is equivalent to dividing by 1.8). x > -5.4 / 1.8

Simplifying: x > -3

So the solution to the second inequality is x > -3.

3. 4(3x - 2) > 6 - 2(5 + 4x): To solve this inequality, let's simplify the expressions first.

Step 1: Distribute the 4 on the left side and the -2 on the right side. 12x - 8 > 6 - 10 - 8x

Step 2: Combine like terms. 12x - 8 > -4 - 8x

Step 3: Add 8x to both sides. 20x - 8 > -4

Step 4: Add 8 to both sides. 20x > 4

Step 5: Divide both sides by 20. x > 4 / 20

Simplifying: x > 0.2

So the solution to the third inequality is x > 0.2.

To summarize:

1. x <= 3
2. x > -3
3. x > 0.2