How do you solve for x in #3x-5

Question

How do you solve for x in #3x-5 < x + 9 \le 5x + 13 #?

Avery Alexander · Accepted Answer

By separating into two inequalities,

#{(3x-5 < x+9),(x+9 le 5x+13):}#

Let us work on the first inequality.

#3x-5 < x+9#

by subtracting #x#,

#=> 2x-5 < 9#

by adding 5,

#=> 2x<14#

by dividing by #2#,

#=> x<7#

Let us work on the second inequality.

#x+9 le 5x+13#

by subtracting #x#,

#=> 9 le 4x+13#

by subtracting #13#,

#=> -4 le 4x#

by dividing by #4#,

#=> -1 le x#

By combining the two inequalities, we have

#-1 le x < 7#,

or in interval notation, the solution set is

#[-1,7)#.

I hope that this was helpful.

Jace Anderson · Answer

undefined To solve for $x$ in the compound inequality $3x - 5 < x + 9 \leq 5x + 13$, follow these steps:

1. First, solve the inequality $3x - 5 < x + 9$:

$$3x - 5 < x + 9$$

2. Subtract $x$ from both sides:

$$2x - 5 < 9$$

3. Add 5 to both sides:

$$2x < 14$$

4. Divide both sides by 2:

$$x < 7$$

So, the solution to the first part of the compound inequality is $x < 7$.

5. Now, solve the inequality $x + 9 \leq 5x + 13$:

$$x + 9 \leq 5x + 13$$

6. Subtract $x$ from both sides:

$$9 \leq 4x + 13$$

7. Subtract 13 from both sides:

$$-4 \leq 4x$$

8. Divide both sides by 4:

$$-1 \leq x$$

So, the solution to the second part of the compound inequality is $-1 \leq x$.

Therefore, the solution to the compound inequality $3x - 5 < x + 9 \leq 5x + 13$ is $-1 \leq x < 7$.

How do you solve for x in #3x-5 &lt; x + 9 \le 5x + 13 #?