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. =3
Just solve these like a basic algebra problem, getting the variable on a side by itself. Let's look at #2.
-4z + 8 < -27 + z
+4z +4z
_________________________
8 < -27 + 5z
+27 +27
_____________________________
35 < 5z
divide both sides by 5 and
7 < z
Check it with a couple of different numbers replacing z to make sure it is right.
Hope this helps! Good luck!
To solve these inequality problems, you need to isolate the variable on one side of the inequality sign. Here's how you can approach each problem:
1) y/2 + 5 > 8:
To isolate the variable 'y', you can start by subtracting 5 from both sides of the inequality:
y/2 > 8 - 5
Simplifying further, y/2 > 3
Now, to solve for 'y', you need to multiply both sides of the inequality by 2 (since there is division by 2 on the left side):
(y/2) * 2 > 3 * 2
y > 6
2) -4z + 8 < -27 + z:
In this inequality, you have two terms with 'z', so the first step is to get all 'z' terms on one side. You can do this by subtracting 'z' from both sides:
-4z + z + 8 < -27
Simplifying further, -3z + 8 < -27
Next, subtract 8 from both sides:
-3z < -27 - 8
Simplifying further, -3z < -35
To solve for 'z', divide both sides of the inequality by -3. However, note that dividing by a negative number changes the direction of the inequality sign, so we need to reverse it:
-3z / -3 > -35 / -3
z > 35/3
3) 3(5 + x) ≤ 18:
Applying the distributive property, you get:
15 + 3x ≤ 18
Next, subtract 15 from both sides of the inequality:
3x ≤ 18 - 15
Simplifying further, 3x ≤ 3
Finally, divide both sides of the inequality by 3 to solve for 'x':
(3x)/3 ≤ 3/3
x ≤ 1
So, the solutions for each of the inequalities are:
1) y > 6
2) z > 35/3
3) x ≤ 1