Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
20∣x−1∣−931
Evaluate
5∣4x−4∣−931
Calculate the absolute value
More Steps
Calculate
∣4x−4∣
Rewrite the expression
∣4(x−1)∣
Rewrite the expression
4∣x−1∣
5×4∣x−1∣−931
Solution
20∣x−1∣−931
Show Solution
Find the roots
x1=−20911,x2=20951
Alternative Form
x1=−45.55,x2=47.55
Evaluate
5∣4x−4∣−931
To find the roots of the expression,set the expression equal to 0
5∣4x−4∣−931=0
Calculate the absolute value
More Steps
Calculate
∣4x−4∣
Rewrite the expression
∣4(x−1)∣
Rewrite the expression
4∣x−1∣
5×4∣x−1∣−931=0
Multiply the terms
20∣x−1∣−931=0
Separate the equation into 2 possible cases
20(x−1)−931=0,x−1≥020(−(x−1))−931=0,x−1<0
Solve the equation
More Steps
Evaluate
20(x−1)−931=0
Calculate
More Steps
Evaluate
20(x−1)−931
Expand the expression
20x−20−931
Subtract the numbers
20x−951
20x−951=0
Move the constant to the right-hand side and change its sign
20x=0+951
Removing 0 doesn't change the value,so remove it from the expression
20x=951
Divide both sides
2020x=20951
Divide the numbers
x=20951
x=20951,x−1≥020(−(x−1))−931=0,x−1<0
Solve the inequality
More Steps
Evaluate
x−1≥0
Move the constant to the right side
x≥0+1
Removing 0 doesn't change the value,so remove it from the expression
x≥1
x=20951,x≥120(−(x−1))−931=0,x−1<0
Solve the equation
More Steps
Evaluate
20(−(x−1))−931=0
Calculate
20(−x+1)−931=0
Calculate
More Steps
Evaluate
20(−x+1)−931
Expand the expression
−20x+20−931
Subtract the numbers
−20x−911
−20x−911=0
Move the constant to the right-hand side and change its sign
−20x=0+911
Removing 0 doesn't change the value,so remove it from the expression
−20x=911
Change the signs on both sides of the equation
20x=−911
Divide both sides
2020x=20−911
Divide the numbers
x=20−911
Use b−a=−ba=−ba to rewrite the fraction
x=−20911
x=20951,x≥1x=−20911,x−1<0
Solve the inequality
More Steps
Evaluate
x−1<0
Move the constant to the right side
x<0+1
Removing 0 doesn't change the value,so remove it from the expression
x<1
x=20951,x≥1x=−20911,x<1
Find the intersection
x=20951x=−20911,x<1
Find the intersection
x=20951x=−20911
Solution
x1=−20911,x2=20951
Alternative Form
x1=−45.55,x2=47.55
Show Solution