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Sagot :
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.
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.
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