How Do You Solve a Word Problem Using an Inequality With Variables on Both Sides?

Summary

'n' is a variable representing the "number" of seeds in Edith's apple
Her pomegranate has one less than three times as many seeds as her apple, or '3n-1'
Her orange has thirteen less than five times as many seeds as her apple, or '5n-13'
We translated "more" into the '>', which also means GREATER THAN
Remember that dividing a negative by a negative will make a positive
The inequality sign flips when we divide by a negative
Edith's apple has LESS THAN 5 seeds
The '<' symbol means LESS THAN

Notes

1. 'n' is a variable representing the "number" of seeds in Edith's apple
2. 'n' is what we are trying to solve for
1. 'n' is a variable representing the "number" of seeds in Edith's apple
2. 'n' is what we are trying to solve for
1. In other words:
2. seeds in pomegranate = 3(seeds in apple) - 1
1. Seeds in apple = n
2. "3 times the number of seeds in her apple" = 3n
1. In other words:
2. seeds in pomegranate = 3n - 1
1. Seeds in pomegranate = 3n - 1
1. Seeds in orange = 5(seeds in apple) - 13
1. Seeds in apple = n
2. "5 times the number of seeds in her apple" = 5n
1. In other words:
2. seeds in orange = 5n - 13
1. Seeds in orange = 5n - 13
1. Pomegranate seeds > Orange seeds
2. The '>' symbol means MORE, or GREATER THAN
1. Pomegranate seeds > Orange seeds
2. The '>' symbol means MORE, or GREATER THAN
3. Seeds in pomegranate = 3n - 1
4. Seeds in orange = 5n - 13
5. At this point, our inequality looks like: '3n-1 > 5n-13'
1. Remember, 'n' represents the "number" of seeds in Edith's apple
2. Solving for 'n' means we just want to get it alone on one side of the inequality
3. At this point, our inequality looks like: '3n-1 > 5n-13'
1. Up to this point, our inequality looks like: '3n-1 > 5n-13'
2. After adding 1 to both sides, our inequality looks like: '3n>5n-12'
1. After adding 1 to both sides, our inequality looks like: '3n>5n-12'
1. Here, we're just combining the like terms, '3n' and '5n'
2. Up to this point, our inequality looks like: '3n>5n-12'
3. After subtracting 5n, our inequality looks like: '-2n>-12'
1. After subtracting 5n, our inequality looks like: '-2n>-12'
1. Up to this point, our inequality looks like: '-2n>-12'
2. After dividing by -2, our inequality looks like: 'n<6'
1. After dividing by -2, our inequality looks like: 'n<6'
2. Remember that dividing a negative by a negative makes a positive
1. After dividing by -2, our inequality looks like: 'n<6'
2. Remember that dividing a negative by a negative makes a positive
1. After dividing by -2, our inequality looks like: 'n<6'
2. Remember that dividing a negative by a negative makes a positive
3. The division property of inequality says we need to flip our inequality symbol if we divide by a negative
1. After dividing by -2, our inequality looks like: 'n<6'
2. Remember that dividing a negative by a negative makes a positive
3. The division property of inequality says we need to flip our inequality symbol if we divide by a negative
4. The '<' symbol means LESS THAN
1. Remember, 'n' represents the "number" of seeds in Edith's apple
2. So we can translate 'n<6' into "Edith's apple has LESS THAN 6 seeds"
3. The '<' symbol means LESS THAN

Edith is counting the number of seeds in her fruit. Her pomegranate has one less than three times as many seeds as her apple. Her orange has thirteen less than five times as many seeds as her apple. If her pomegranate has more seeds than her orange, how many seeds are there in Edith's apple?

Summary

Notes