Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
35<x<3
Alternative Form
x∈(35,3)
Evaluate
∣2x−4∣<x−1
Simplify
More Steps
Evaluate
∣2x−4∣
Rewrite the expression
∣2(x−2)∣
Rewrite the expression
2∣x−2∣
2∣x−2∣<x−1
Transform the expression
2(x−2)<x−1,x−2≥02(−x+2)<x−1,x−2<0
Calculate
More Steps
Calculate
2(x−2)<x−1
Expand the expression
More Steps
Evaluate
2(x−2)
Apply the distributive property
2x−2×2
Multiply the numbers
2x−4
2x−4<x−1
Move the expression to the left side
2x−4−x<−1
Move the expression to the right side
2x−x<−1+4
Add and subtract
More Steps
Evaluate
2x−x
Collect like terms by calculating the sum or difference of their coefficients
(2−1)x
Subtract the numbers
x
x<−1+4
Add and subtract
x<3
x<3,x−2≥02(−x+2)<x−1,x−2<0
Calculate
More Steps
Calculate
x−2≥0
Move the constant to the right side
x≥0+2
Removing 0 doesn't change the value,so remove it from the expression
x≥2
x<3,x≥22(−x+2)<x−1,x−2<0
Calculate
More Steps
Calculate
2(−x+2)<x−1
Expand the expression
More Steps
Evaluate
2(−x+2)
Apply the distributive property
2(−x)+2×2
Multiply the numbers
−2x+2×2
Multiply the numbers
−2x+4
−2x+4<x−1
Move the expression to the left side
−2x+4−x<−1
Move the expression to the right side
−2x−x<−1−4
Add and subtract
More Steps
Evaluate
−2x−x
Collect like terms by calculating the sum or difference of their coefficients
(−2−1)x
Subtract the numbers
−3x
−3x<−1−4
Add and subtract
−3x<−5
Change the signs on both sides of the inequality and flip the inequality sign
3x>5
Divide both sides
33x>35
Divide the numbers
x>35
x<3,x≥2x>35,x−2<0
Calculate
More Steps
Calculate
x−2<0
Move the constant to the right side
x<0+2
Removing 0 doesn't change the value,so remove it from the expression
x<2
x<3,x≥2x>35,x<2
Calculate
2≤x<3x>35,x<2
Solution
35<x<3
Alternative Form
x∈(35,3)
Show Solution
