can you walk me through these
4+x/5 < 8
and
x-2/3> 2x + 11
Treat inequality just like an equation, except when you multiply or divide by a negative number, which means you have to reverse the carat.
Subtract 4 from both sides.
x/5 < 4
Multiply both sides by 5.
x < 20
Now you try the second inequality.
I tried the second one and did not get
-7 which is the answer
and 36 is the answer to the first one. Am I missing some steps. Help
Of course! I'll walk you through solving each of these inequalities step by step.
First, let's start with the inequality 4 + x/5 < 8.
Step 1: To eliminate the fraction, we can multiply both sides of the inequality by 5, since the denominator is 5. This will give us:
5 * (4 + x/5) < 5 * 8
Simplifying this, we have:
20 + x < 40
Step 2: Next, let's isolate the variable x. To do this, we subtract 20 from both sides of the inequality:
20 + x - 20 < 40 - 20
Simplifying further:
x < 20
Therefore, the solution to the inequality 4 + x/5 < 8 is x < 20.
Now let's move on to the second inequality: x - 2/3 > 2x + 11
Step 1: To eliminate the fraction, we can multiply both sides of the inequality by 3, since the denominator is 3. This will give us:
3 * (x - 2/3) > 3 * (2x + 11)
Simplifying this, we have:
3x - 2 > 6x + 33
Step 2: Next, let's isolate the variable x. To do this, we subtract 3x from both sides of the inequality:
3x - 2 - 3x > 6x + 33 - 3x
Simplifying further:
-2 > 3x + 33
Step 3: Now, subtract 33 from both sides of the inequality to further isolate x:
-2 - 33 > 3x + 33 - 33
Simplifying:
-35 > 3x
Step 4: Finally, divide both sides of the inequality by 3 to solve for x:
(-35)/3 > (3x)/3
Simplifying further:
x < -35/3
Therefore, the solution to the inequality x - 2/3 > 2x + 11 is x < -35/3.
I hope this explanation helps! Let me know if you have any further questions.