# 1 2 x + 3 < 4x - 7

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

Solve inequalities is no different than solving regular equations.  In both cases, you need to get all the x terms on one side of the equation and all the numbers on the other.

One way to do this question is this:

Subtract 4x from both sides.  You now have

-3.5x + 3 < -7

Subtract 3 from both sides

-3.5x < -10

Divide both sides by -3.5.  Be sure to switch the direction of the inequality sign.

x > 2.85

If you prefer, you can multiply both sides by 2 to get your .5x to be x.

x + 6 < 8x - 14

Then you move the 8x and the 6.

-7x < -20

Again, be sure to switch the direction of the inequality sign.

x > 20/7

or

x > 2.85

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

For solving the inequality, we'll move 4x to the left side and the free term to the right side:

(1/2)x-4x<-3-7

In order to do the calculations, we'll have to have the same denominator, which is 2. For this reason, we'll amplify each term, except the ratio (1/2)x, with 2.

(1/2)x-(8/2)x<-20/2

-(7/2)x<-10

We'll multiply with (-1)  and the direction of inequality will be changed:

(7/2)x>10

x>10*2/7

x>20/7

x belongs to the set (20/7, +inf)