Question

Which set expresses the solution to the compound inequality -3 ≤ 4x+7/5 + 2 < 4?

{x : -8 ≤ x < 10}
{x : -5/4 ≤ x < 10}
{x : -8 ≤ x < 3/4}
{x : -9 ≤ x < 3/4}

Answer 1

Interpret the expression as (4x+7)/5 + 2. Solve

-3 ≤ (4x+7)/5 + 2 < 4.

Subtract 2: -5 ≤ (4x+7)/5 < 2.

Multiply by 5: -25 ≤ 4x+7 < 10.

Subtract 7: -32 ≤ 4x < 3.

Divide by 4: -8 ≤ x < 3/4.

So the solution set is {x : -8 ≤ x < 3/4}.