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If 3x+7lt5x-4, which of the following is...

If `3x+7lt5x-4`, which of the following is true?

A

`(11)/(2)ltx`

B

`xlt(3)/(2)`

C

`xlt(11)/(8)`

D

`(11)/(2)gtx`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the inequality \(3x + 7 < 5x - 4\), we will follow these steps: ### Step 1: Rearrange the inequality We start with the given inequality: \[ 3x + 7 < 5x - 4 \] We want to isolate \(x\) on one side. First, we can move \(3x\) to the right side and \(-4\) to the left side. ### Step 2: Move terms Subtract \(3x\) from both sides: \[ 7 < 5x - 3x - 4 \] This simplifies to: \[ 7 < 2x - 4 \] ### Step 3: Add 4 to both sides Next, we add \(4\) to both sides to isolate the term with \(x\): \[ 7 + 4 < 2x \] This simplifies to: \[ 11 < 2x \] ### Step 4: Divide by 2 Now, we divide both sides by \(2\) to solve for \(x\): \[ \frac{11}{2} < x \] ### Step 5: Rewrite the inequality This can be rewritten as: \[ x > \frac{11}{2} \] ### Conclusion Thus, the solution to the inequality is: \[ x > \frac{11}{2} \] This means that \(x\) must be greater than \(5.5\).
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Knowledge Check

  • 3x+b =5x-7 3y + c= 5y-7 In the equation above, b and c are constants. If b is c minus 1/2 , which of the following is true?

    A
    x is y minus `1/4`
    B
    x is y minus `1/2`
    C
    x is minus 1.
    D
    x is y plus `1/2`.

  • If -3lt2x+4lt9 , which of the following CANNOT be a possible value of x?

    A
    `-2`
    B
    `-4`
    C
    `0`
    D
    `2`

  • Based on the graph in the previous example, which of the following statements must be true I. f(5)+f(-5)=0 . (II. 9f -5 lt x lt 5 , the maximum value of function f is 4. III. The quation f(x)=3 has 3 real solution.

    A
    I only
    B
    II only
    C
    I and II only
    D
    II and III only

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