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Solve the inequality

Solve the inequality-example-1

2 Answers

3 votes

Answer:

x<=-11/4

Explanation:

To solve the inequality -3 >= -1 - 3/2(-4x + 9), we can follow these steps:

1. Start by simplifying the expression on the right side of the inequality.

-1 - 3/2(-4x + 9) can be rewritten as -1 + (3/2)(4x - 9) using the distributive property.

-1 + (3/2)(4x - 9) simplifies further to -1 + (3/2)(4x) - (3/2)(9) by distributing (3/2) to (4x - 9).

-1 + (3/2)(4x) - (3/2)(9) simplifies to -1 + (6x) - (27/2) by multiplying (3/2) with 4x and 9.

Combining like terms, we get -1 + 6x - 27/2.

2. Now we can rewrite the inequality as -3 >= -1 + 6x - 27/2.

3. To isolate the variable, we can subtract -1 and -27/2 from both sides of the inequality.

-3 - (-1) >= -1 + 6x - 27/2 - (-1) - (-27/2)

-3 + 1 >= -1 + 6x + 1 + 27/2

-2 >= 6x + 29/2

4. Next, we can simplify the expression on the right side of the inequality.

6x + 29/2 can be rewritten as 6x + (29/2).

5. Now we can rewrite the inequality as -2 >= 6x + 29/2.

6. To isolate the variable, we can subtract (29/2) from both sides of the inequality.

-2 - (29/2) >= 6x + 29/2 - (29/2)

-2 - (29/2) >= 6x

7. Simplifying the expression on the left side of the inequality gives:

-4/2 - 29/2 >= 6x

-33/2 >= 6x

8. Finally, we can solve for x by dividing both sides of the inequality by 6.

(-33/2) / 6 >= x

-33/12 >= x

-11/4 >= x

So, the solution to the inequality -3 >= -1 - 3/2(-4x + 9) is x ≤ -11/4.

User Fonebone
by
8.2k points
5 votes

Answer:

Step-by-step explanation: 4 divided by 5. Put the one on top of the 4 then put a one below the 5. Now you should have 1/4 divided by 5/1. times the 4 and 1. That is 4, now times 1 and 5 that’s 5. So your left with the answer 4/5

User Isura Nirmal
by
8.2k points

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