How do you do these problems...
1) y/2+5>8
2) -4z+8<-27+z
3) 3(5+x)<_18
I need help mostly on #2 but also on the others. Oh and on #3 the sign is an less than or equal to sign.
Treat the inequality like an equation. The only exception is when you multiply/divide both sides by a negative number. Then the inequality reverses.
-4z+8<-27+z
Add 4z and 27 to both sides.
35 < 5z
The "less than or equal" sign can be obtained by pressing your <alt/option> key along with the <comma> key (at least on a Mac). Likewise, the "more than or equal" sign can be obtained by pressing your <alt/option> key along with the <period> key.
3(5+x)≤18
Divide both sides by 3.
5 + x ≤ 6
y/2+5>8
Mulitply both sides by 2.
y + 10 > 16
You should be able to take them from here.
I hope this helps. Thanks for asking.
Sure! Let's break down each problem step by step.
1) y/2 + 5 > 8:
To solve this inequality, we need to isolate the variable (y) on one side of the inequality.
Step 1: Subtract 5 from both sides:
y/2 > 8 - 5
y/2 > 3
Step 2: Multiply both sides by 2 (to cancel out the division):
y > 3 * 2
y > 6
So the solution for this inequality is y > 6.
2) -4z + 8 < -27 + z:
To solve this inequality, we need to gather the variables (z) on one side of the inequality.
Step 1: Subtract z from both sides:
-4z - z + 8 < -27
Step 2: Combine like terms:
-5z + 8 < -27
Step 3: Subtract 8 from both sides:
-5z + 8 - 8 < -27 - 8
-5z < -35
Step 4: Divide both sides by -5 (Note: since we divide by a negative number, the inequality sign flips):
-5z / -5 > -35 / -5
z > 7
So the solution for this inequality is z > 7.
3) 3(5 + x) <= 18:
To solve this inequality, we need to simplify and isolate the variable (x) on one side of the inequality.
Step 1: Distribute the 3 to the terms inside the parentheses:
15 + 3x <= 18
Step 2: Subtract 15 from both sides:
15 - 15 + 3x <= 18 - 15
3x <= 3
Step 3: Divide both sides by 3:
3x / 3 <= 3 / 3
x <= 1
So the solution for this inequality is x <= 1.
I hope this helps! Let me know if you have any further questions.