Question

Solve the compound inequality -4< 3x-5/2 + 3 =< 10

Answer 1

• -3 < x ≤ 6 1/3 or x ∈ (-3; 6 1/3]

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Solution in below steps:

• -4 < (3x - 5)/2 + 3 ≤ 10
• -4 - 3 < (3x - 5)/2 ≤ 10 - 3 Add - 3 to all sides
• -7 < (3x - 5)/2 ≤ 7
• -7*2 < 3x - 5 ≤ 7*2 Multiply all sides by 2
• - 14 < 3x - 5 ≤ 14
• -14 + 5 < 3x ≤ 14 + 5 Add 5 to all sides
• -9 < 3x ≤ 19
• -9/3 < x ≤ 19/3 Divide all sides by 3
• -3 < x ≤ 6 1/3 Answer as simple inequality

or

• x ∈ (-3; 6 1/3] Answer as interval