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#### OneidaFL

The post reads: If you replace the equal sign of an equation with the inequality sign, there is never a time when the same value will be a solution to both, namely due to the fact that a solution less than or greater than never be equal to the same solution.

Solve: 6x + 7 > 15 x = 1 Can this be solved with the factor given for X. I do not think so, How am I suppose to solve this can someone help me to understand the steps that are needed to solve this inequality

#### skeeter

MHF Helper
The post reads: If you replace the equal sign of an equation with the inequality sign, there is never a time when the same value will be a solution to both, namely due to the fact that a solution less than or greater than never be equal to the same solution.

Solve: 6x + 7 > 15 x = 1 Can this be solved with the factor given for X. I do not think so, How am I suppose to solve this can someone help me to understand the steps that are needed to solve this inequality
I'm assuming the "equal sign" is a typo ... do you mean the inequality

$$\displaystyle 6x+7 > 15x+1$$ ?

if so ...

subtract $$\displaystyle 6x$$ and $$\displaystyle 1$$ from both sides ...

$$\displaystyle 6 > 9x$$

divide both sides by $$\displaystyle 9$$

$$\displaystyle \frac{6}{9} > x$$

reduce and rewrite ...

$$\displaystyle x < \frac{2}{3}$$

#### rtblue

Sorry. I didn't not recognize that the = sign would be a +. I agree with skeeter.

#### OneidaFL

unfortunately I think that the student was trying to give the value of x=1 for the following

#### OneidaFL

Correction for inequality question

This is the actual problem: 6x + 7 > 15

I need to know how to figure this out. The student had given the value of x to be 1. That just doesn't make sense to me.

Thank You!

#### pickslides

MHF Helper
$$\displaystyle 6x + 7 > 15$$

$$\displaystyle 6x + 7 {\color{red}-7}> 15{\color{red}-7}$$

$$\displaystyle 6x > 8$$

$$\displaystyle \frac{6x}{{\color{red}6}} > \frac{8}{{\color{red}6}}$$

$$\displaystyle x > \frac{8}{6} \approx 1.33$$

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#### Keep

unfortunately I think that the student was trying to give the value of x=1 for the following
The solution is the same as you would do for equation. If you had $$\displaystyle 6x +7 = 15$$ how would you solve?

I guess you would do this.

$$\displaystyle 6x+7 = 15$$
$$\displaystyle 6x = 15-7$$

$$\displaystyle x = 8/6 = 4/3$$

Now it is the same for inequality.

$$\displaystyle 6x+7 > 15$$ meanining $$\displaystyle 6x > 15-7$$, meaning $$\displaystyle 6x > 8$$, meaning $$\displaystyle x > 4/3$$

#### skeeter

MHF Helper
most probably, the longest thread I've seen over a linear inequality. (Wondering)

• mr fantastic

#### mr fantastic

MHF Hall of Fame
most probably, the longest thread I've seen over a linear inequality. (Wondering)
And it ain't gettin' any longer.