How do you solve 2x+3>7 or 2x+9>11?

Question

How do you solve 2x+3>7 or 2x+9>11?

1 Answer

Impact of this question

14087 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-31T04:13:56

The solution set is ${x ∣ x > 1}$ ${x | x>1}$ .

Explanation:

For each of these inequalities, there will be a set of $x$ $x$ -values that make them true. For example, it's pretty clear that large values of $x$ $x$ (like 1,000) work for both, and negative values (like -1,000) will not work for either.

Since we're asked to solve a "this OR that" pair of inequalities, what we'd like to know are all the $x$ $x$ -values that will work for at least one of them. To do this, we solve both inequalities for $x$ $x$ , and then overlap the two solution sets.

Inequality 1:

$2 x + 3 > 7 \Rightarrow 2 x > 4$ $2x+3>7" "=>" "2x>4" "$ (subtract 3 from both sides)
$2 x + 3 > 7 \Rightarrow x > 2$ $color(white)(2x+3>7)" "=>" "x>2" "$ (divide both sides by 2)

Inequality 2:

$2 x + 9 > 11 \Rightarrow 2 x > 2$ $2x+9>11" "=>" "2x>2" "$ (subtract 9 from both sides)
$2 x + 9 > 11 \Rightarrow x > 1$ $color(white)(2x+9>11)" "=>" "x>1" "$ (divide both sides by 2)

So we need to list all the $x$ $x$ -values that satisfy either $x > 2$ $x>2$ or $x > 1$ $x>1$ .

In this case, if an $x$ $x$ -value is greater than 2, it will automatically be greater than 1. Thus, the solution set for $2 x + 3 > 7$ $2x+3>7$ is a subset of the one for $2 x + 9 > 11$ $2x+9>11$ . That means, all we need to do here is list the solution set for $2 x + 9 > 11$ $2x+9>11$ , and we're done.

The solution set we need is simply "all $x$ $x$ such that $x$ $x$ is greater than 1", or (in math terms):

${x ∣ x > 1}$ ${x | x>1}$
or
$x \in (1, \infty)$ $x in (1, oo)$

Science

Math

Humanities

... and beyond

How do you solve 2x+3>7 or 2x+9>11?

1 Answer

Explanation:

Related questions

Impact of this question