Solve for 2 and graph the solution on the number line below. 1>-x - 1 and -х 1 -13
To solve the inequality 1 > -x - 1, we can start by isolating the x variable.
1 > -x - 1
1 + 1 > -x
2 > -x
To solve the inequality -х + 1 < -13, we isolate the x variable:
-х + 1 < -13
-х < -13 -1
-х < -14
Since we multiplied by a negative number, we want to flip the inequality sign:
x > 14
Now, let's graph the solutions on a number line:
-----------------------------[0]------------------[14]---------------------
Since the first inequality is 2 > -x, we can rewrite it as -x < 2. When we multiply or divide by a negative number, we flip the inequality sign:
-x < 2
x > -2
So we graph the solution x > -2 as an open circle at -2 with an arrow pointing to the right.
-----------------------------(-2)---->[0]------------------[14]---------------------
For the second inequality x > 14, we graph this as an open circle at 14 with an arrow pointing to the right.
-----------------------------(-2)---->[0]-(14)---->---------------------
The solution to both inequalities, when combined, is x > 14.
-----------------------------(-2)---->[0]-------(14)---->---------------------