1) First expand the brackets.
Multiply everything in the brackets by the number outside the brackets (3)
3 x m = 3m
3 x 4 = 12
Now we have:
3m - 12 < 27
Now we have to isolate the x. We can do this by removing the 12 by adding 12 to make it 0, and whatever we do to on side of the equation we must do to the other side.
-12 + 12 = 0
27 + 12 = 39
Now we have:
3x > 39
To isolate the x completely, we divide it by 3, and we divide 39 by 3 as well.
3x ÷ 3 = x
39 ÷ 3 = 13
Answer: x > 13
2: We can do the same thing here even though it looks different.
Isolate the x by subtracting 7, do this on the other side of the equation.
We now have
-20 < 4x
Divide both 4 and 20 by 4. To get x by itself.
-20 ÷ 4 = -5
4x ÷ 4 = x
Answer: x > -5
3: Same thing. Isolate x by subtracting 7 on both sides of the equation.
7 - 7 = 0
19 - 7 = 12
New equation
2x = 12
Divide both sides by 2
2x ÷ 2 = x
12 ÷ 2 = 6
Answer: x < 6
4: Expand the brackets first.
5 x p = 5p
5 x -2 = -10
New equation:
-45 < 5p - 10
Isolate p by adding 10 by both sides. Since -10 is negative, we add a positive number to make it 0.
-10 + 10 = 0
-45 + 10 = -35
New equation:
-35 > 5p
Divide 5 by both 5p and -35 to isolate p.
5p ÷ 5 = p
-35 ÷ 5 = -7
Answer: -7 > p or p < -7 (doesn't matter)
5) Expand the brackets.
-7 × x = -7x
-7 × -2 = 14
New equation:
21 < -7x + 14
Isolate x by subtracting 14 to both sides of the equation again.
14 - 14 = 0
21 - 14 = 7
New equation:
7 < -7x
Divide both sides by 7 to isolate x completely.
-7x ÷ 7 = -x
7 ÷ 7 = 1
Answer = 1 < -x or -x > 1
Doesn't matter if x is negative.
If it does, just switch the negative symbol from x to 1.
So x > -1