To solve the inequality [tex]\( 5w > -6w + 11 \)[/tex] for [tex]\( w \)[/tex], we can follow these steps:
1. Isolate the variable [tex]\( w \)[/tex] on one side of the inequality.
We start by adding [tex]\( 6w \)[/tex] to both sides to combine the [tex]\( w \)[/tex] terms on one side. This will eliminate [tex]\( -6w \)[/tex] on the right side:
[tex]\[
5w + 6w > -6w + 6w + 11
\][/tex]
Simplifying both sides gives:
[tex]\[
11w > 11
\][/tex]
2. Solve for [tex]\( w \)[/tex] by dividing both sides of the inequality by 11:
[tex]\[
\frac{11w}{11} > \frac{11}{11}
\][/tex]
Simplifying this, we get:
[tex]\[
w > 1
\][/tex]
Therefore, the solution to the inequality [tex]\( 5w > -6w + 11 \)[/tex] is:
[tex]\[
w > 1
\][/tex]
This means that [tex]\( w \)[/tex] must be greater than 1.
