Question

Solve the inequality 7/2 > b + 9/5

Answer 1

7/2 > b + 9/5

-9/5 -9/5

7/2-9/5>b

35/10-18/10>b

17/10>b

1 7/10 > b

b<17/10

b<1 7/10

I rewrote the inequality in many forms just in case if you needed it. The bolded forms are all the same except two have improper fractions, two have mixed numbers, and the b is on the right hand side for two whereas in the other two b is on the left hand side.

Explanation:

Answer 2

b < 17/10

Knowledge Needed

To solve, you must isolate the variable. It means moving the variable and it's coefficient to the other side of the equation by itself.

Rule

If you multiply, divide, add, subtract, square root, exponent both sides of the equation by the same value, that end value stays the same. That is how you solve for it.

However, if you divide or multiply by a negative number by both sides in an inequality, you must flip the sign.

For example:

> to <

`\geq` to
`\leq`

Question

Subtract 9/5 on both sides.

7/2 - 9/5 > b + 9/5 - 9/5

Combine like terms,

7/2 - 9/5 > b

Find the LCD of 7/2 and 9/5 to solve.

LCM of 2 and 5: 10

Multiply both top and bottom of both fractions by 10/their denominator.

35/10 - 18/10 > b

17/10 > b

b < 17/10