Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈(−∞,−85]∪[813,+∞)
Evaluate
∣8x−4∣−4≥5
Calculate the absolute value
More Steps
Evaluate
∣8x−4∣
Rewrite the expression
∣4(2x−1)∣
Rewrite the expression
4∣2x−1∣
4∣2x−1∣−4≥5
Move the expression to the left side
4∣2x−1∣−4−5≥0
Subtract the numbers
4∣2x−1∣−9≥0
Rewrite the expression
4∣2x−1∣≥9
Divide both sides
44∣2x−1∣≥49
Divide the numbers
∣2x−1∣≥49
Separate the inequality into 2 possible cases
2x−1≥492x−1≤−49
Solve the inequality for x
More Steps
Evaluate
2x−1≥49
Move the constant to the right side
2x≥49+1
Add the numbers
More Steps
Evaluate
49+1
Reduce fractions to a common denominator
49+44
Write all numerators above the common denominator
49+4
Add the numbers
413
2x≥413
Multiply by the reciprocal
2x×21≥413×21
Multiply
x≥413×21
Multiply
More Steps
Evaluate
413×21
To multiply the fractions,multiply the numerators and denominators separately
4×213
Multiply the numbers
813
x≥813
x≥8132x−1≤−49
Solve the inequality for x
More Steps
Evaluate
2x−1≤−49
Move the constant to the right side
2x≤−49+1
Add the numbers
More Steps
Evaluate
−49+1
Reduce fractions to a common denominator
−49+44
Write all numerators above the common denominator
4−9+4
Add the numbers
4−5
Use b−a=−ba=−ba to rewrite the fraction
−45
2x≤−45
Multiply by the reciprocal
2x×21≤−45×21
Multiply
x≤−45×21
Multiply
More Steps
Evaluate
−45×21
To multiply the fractions,multiply the numerators and denominators separately
−4×25
Multiply the numbers
−85
x≤−85
x≥813x≤−85
Solution
x∈(−∞,−85]∪[813,+∞)
Show Solution
