7|x+2|+5>4

Michael Maggard
2021-12-09
Answered

Solve the inequality.

7|x+2|+5>4

7|x+2|+5>4

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Rita Miller

Answered 2021-12-10
Author has **28** answers

Step 1

We can solve the absolute value inequality by adding , subtracting , multiplying and dividing with constants . The important thing is that if we multiply or divide by using any negative number, then the absolute inequality reverses .

The absolute inequality can be solved by using the formula ,

If$|x-a|\le r$ , then $-r\le x-a\le r$ ,

$|x-a|\ge r$ , then $|x-a|\le -r$

Also we use the form that |x|=|-x|=x .

Step 2

Consider the absolute inequality 7|x+2|+5>4,

We can start solving the inequality by subtracting 5 on both side,

7|x+2|+5-5>4-5

7|x+2|>-1

Now divide by 7 on both sides, we get

$\frac{7|x+2|}{7}>\frac{-1}{7}$

$|x+2|>\frac{-1}{7}$

Thus in the last inequality , For any x both positive and negative we only get positive value from the absolute equation,

We know that |x|=|-x|=x,

There for any real number$|x+2|>\frac{-1}{7}$ is true.

Thus x can be any real number$x\in R$ , where R denoting real numbers .

Hence the interval form of the solution is$x\in (-\mathrm{\infty},\mathrm{\infty})$ .

We can solve the absolute value inequality by adding , subtracting , multiplying and dividing with constants . The important thing is that if we multiply or divide by using any negative number, then the absolute inequality reverses .

The absolute inequality can be solved by using the formula ,

If

Also we use the form that |x|=|-x|=x .

Step 2

Consider the absolute inequality 7|x+2|+5>4,

We can start solving the inequality by subtracting 5 on both side,

7|x+2|+5-5>4-5

7|x+2|>-1

Now divide by 7 on both sides, we get

Thus in the last inequality , For any x both positive and negative we only get positive value from the absolute equation,

We know that |x|=|-x|=x,

There for any real number

Thus x can be any real number

Hence the interval form of the solution is

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