how would you solve: 4(x-3)<10?

Solution 1::

4(x-3) < 10

Divide both sides by 4

(x-3) < 2.5 because 10/4 = 2.5 (10/4=5/2=2.5)

adding 3 to both the sides

x < 5.5 (=11/2 , or 5/2 + 3 = 5/2 + 6/2 = 11/2)
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or

4(x-3) < 10
4x - 12 < 10
4x < 22
x < 22/2
x< 5.5
Hope that Helps

4(x - 3) < 10
x - 3 < 5/2
x < 5/2 + 6/2
x < 11/2

Answer: x < 11/2 or 5 1/2

4(x - 3) < 10
2(x - 3) < 5
2x - 6 < 5
2x < 11
x < 11/2

4(x - 3) < 10
4*x - 4*3 < 10
4x - 12 < 10
4x < 10 + 12
4x < 22
x < 22/4
x < 11/2 (5.5)

4x - 12 < 10
4x < 22
x < 22 / 4
x < 11 / 2

Don't forget to solve it the other way as well 4(x-3)>-10. You need to check for a minimum of three points on the number line to determine the values of X for which this statement is true.

Divide the inequality by four, and since 4 is positive, inequality sign stays the way it is, so you have
x - 3 < 10/4
x < 10/4 + 3
x < 22/4

Just expand and rearrange:

4x - 12 < 10
4x < 22
x < 5.5