Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
−411<x≤4
Alternative Form
x∈(−411,4]
Evaluate
−17<2(2x−3)≤10
Separate into two inequalities
{−17<2(2x−3)2(2x−3)≤10
Solve the inequality
More Steps
Evaluate
−17<2(2x−3)
Swap the sides of the inequality
2(2x−3)>−17
Divide both sides
22(2x−3)>2−17
Divide the numbers
2x−3>2−17
Use b−a=−ba=−ba to rewrite the fraction
2x−3>−217
Move the constant to the right side
2x>−217+3
Add the numbers
More Steps
Evaluate
−217+3
Reduce fractions to a common denominator
−217+23×2
Write all numerators above the common denominator
2−17+3×2
Multiply the numbers
2−17+6
Add the numbers
2−11
Use b−a=−ba=−ba to rewrite the fraction
−211
2x>−211
Multiply by the reciprocal
2x×21>−211×21
Multiply
x>−211×21
Multiply
More Steps
Evaluate
−211×21
To multiply the fractions,multiply the numerators and denominators separately
−2×211
Multiply the numbers
−411
x>−411
{x>−4112(2x−3)≤10
Solve the inequality
More Steps
Evaluate
2(2x−3)≤10
Divide both sides
22(2x−3)≤210
Divide the numbers
2x−3≤210
Divide the numbers
More Steps
Evaluate
210
Reduce the numbers
15
Calculate
5
2x−3≤5
Move the constant to the right side
2x≤5+3
Add the numbers
2x≤8
Divide both sides
22x≤28
Divide the numbers
x≤28
Divide the numbers
More Steps
Evaluate
28
Reduce the numbers
14
Calculate
4
x≤4
{x>−411x≤4
Solution
−411<x≤4
Alternative Form
x∈(−411,4]
Show Solution
