we are given an OR. A certain x-value is a solution to the statement if it satisfies either of the inequalities. Therefore, the solution to this statement is the union of the solutions of both inequalities. In other words, the entire collection of the solutions of both inequalities forms the solution of this statement.
- 11x+4<15 OR 12x-7>-25, First, you will need to solve the equation to graph the equation.
- 11x+4<15, Subtract 4 on both sides, so you will do this 11x+4-4<15-4 ----> 11x<11. the two fours cancel each other out.
- 11x<11, The final part is that you must DIVIDE each side of the equation, so 11x/11<11/11 -----> x<1
- Now do the other inequality, 12x-7<-25. ADD 7 to each side because you want to cancel out the -7.
- After you do that it should look like this -----> 12x>-18
- Finally, you will divide each side by 12 and then you reduce. 12x/12>-12/18 (Divide 12/18 by 3) -----> x>-3/2
Now, you will have to make a number line ranging from -3 to 3 (Look up a number line if you need to): <--3---2---1--0--1--2--3->
Now, draw OPEN circles over 1 and -1.5 (it's in between -2 and -1) After that DRAW A LINE whichever way the greater/less than sign is facing (So like if it's facing >, then draw your line to the right, this also goes for the one facing left <.)
Lastly, you can see that the lines cross over each other and covers the whole line. Since this is an OR statement the answer is... THE SOLUTION IS ALL VALUES OF X.
