Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
1≤a≤35
Alternative Form
a∈[1,35]
Evaluate
6a−2−210−6a≥0
Find the domain
More Steps
Evaluate
10−6a≥0
Move the constant to the right side
−6a≥0−10
Removing 0 doesn't change the value,so remove it from the expression
−6a≥−10
Change the signs on both sides of the inequality and flip the inequality sign
6a≤10
Divide both sides
66a≤610
Divide the numbers
a≤610
Cancel out the common factor 2
a≤35
6a−2−210−6a≥0,a≤35
Move the expression to the right side
−210−6a≥−6a+2
Divide both sides
10−6a≤3a−1
Separate the inequality into 2 possible cases
10−6a≤3a−1,3a−1≥010−6a≤3a−1,3a−1<0
Solve the inequality
More Steps
Solve the inequality
10−6a≤3a−1
Square both sides of the inequality
10−6a≤(3a−1)2
Move the expression to the left side
10−6a−(3a−1)2≤0
Calculate
More Steps
Evaluate
10−6a−(3a−1)2
Expand the expression
10−6a−9a2+6a−1
Subtract the numbers
9−6a−9a2+6a
The sum of two opposites equals 0
9+0−9a2
Remove 0
9−9a2
9−9a2≤0
Rewrite the expression
−9a2≤−9
Change the signs on both sides of the inequality and flip the inequality sign
9a2≥9
Divide both sides
99a2≥99
Divide the numbers
a2≥99
Divide the numbers
More Steps
Evaluate
99
Reduce the numbers
11
Calculate
1
a2≥1
Take the 2-th root on both sides of the inequality
a2≥1
Calculate
∣a∣≥1
Separate the inequality into 2 possible cases
a≥1a≤−1
Find the union
a∈(−∞,−1]∪[1,+∞)
a∈(−∞,−1]∪[1,+∞),3a−1≥010−6a≤3a−1,3a−1<0
Solve the inequality
More Steps
Evaluate
3a−1≥0
Move the constant to the right side
3a≥0+1
Removing 0 doesn't change the value,so remove it from the expression
3a≥1
Divide both sides
33a≥31
Divide the numbers
a≥31
a∈(−∞,−1]∪[1,+∞),a≥3110−6a≤3a−1,3a−1<0
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of a
a∈(−∞,−1]∪[1,+∞),a≥31a∈∅,3a−1<0
Solve the inequality
More Steps
Evaluate
3a−1<0
Move the constant to the right side
3a<0+1
Removing 0 doesn't change the value,so remove it from the expression
3a<1
Divide both sides
33a<31
Divide the numbers
a<31
a∈(−∞,−1]∪[1,+∞),a≥31a∈∅,a<31
Find the intersection
a≥1a∈∅,a<31
Find the intersection
a≥1a∈∅
Find the union
a≥1
Check if the solution is in the defined range
a≥1,a≤35
Solution
1≤a≤35
Alternative Form
a∈[1,35]
Show Solution
