Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x≥21
Alternative Form
x∈[21,+∞)
Evaluate
x×7≥∣5−3x∣
Use the commutative property to reorder the terms
7x≥∣5−3x∣
Swap the sides
∣5−3x∣≤7x
Rearrange the terms
∣5−3x∣−7x≤0
Separate the inequality into 2 possible cases
5−3x−7x≤0,5−3x≥0−(5−3x)−7x≤0,5−3x<0
Evaluate
More Steps
Evaluate
5−3x−7x≤0
Simplify the expression
5−10x≤0
Move the constant to the right side
−10x≤0−5
Removing 0 doesn't change the value,so remove it from the expression
−10x≤−5
Change the signs on both sides of the inequality and flip the inequality sign
10x≥5
Divide both sides
1010x≥105
Divide the numbers
x≥105
Cancel out the common factor 5
x≥21
x≥21,5−3x≥0−(5−3x)−7x≤0,5−3x<0
Evaluate
More Steps
Evaluate
5−3x≥0
Move the constant to the right side
−3x≥0−5
Removing 0 doesn't change the value,so remove it from the expression
−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≥21,x≤35−(5−3x)−7x≤0,5−3x<0
Evaluate
More Steps
Evaluate
−(5−3x)−7x≤0
Remove the parentheses
−5+3x−7x≤0
Simplify the expression
−5−4x≤0
Move the constant to the right side
−4x≤0+5
Removing 0 doesn't change the value,so remove it from the expression
−4x≤5
Change the signs on both sides of the inequality and flip the inequality sign
4x≥−5
Divide both sides
44x≥4−5
Divide the numbers
x≥4−5
Use b−a=−ba=−ba to rewrite the fraction
x≥−45
x≥21,x≤35x≥−45,5−3x<0
Evaluate
More Steps
Evaluate
5−3x<0
Move the constant to the right side
−3x<0−5
Removing 0 doesn't change the value,so remove it from the expression
−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≥21,x≤35x≥−45,x>35
Find the intersection
21≤x≤35x≥−45,x>35
Find the intersection
21≤x≤35x>35
Solution
x≥21
Alternative Form
x∈[21,+∞)
Show Solution
