Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x∈∅
Alternative Form
No solution
Evaluate
∣x−3∣−2=−∣x∣×3
Multiply the terms
∣x−3∣−2=−3∣x∣
Move the expression to the left side
∣x−3∣−2−(−3∣x∣)=0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
∣x−3∣−2+3∣x∣=0
Separate the equation into 4 possible cases
x−3−2+3x=0,x−3≥0,x≥0x−3−2+3(−x)=0,x−3≥0,x<0−(x−3)−2+3x=0,x−3<0,x≥0−(x−3)−2+3(−x)=0,x−3<0,x<0
Solve the equation
More Steps
Evaluate
x−3−2+3x=0
Calculate the sum or difference
More Steps
Evaluate
x−3−2+3x
Add the terms
4x−3−2
Subtract the numbers
4x−5
4x−5=0
Move the constant to the right-hand side and change its sign
4x=0+5
Removing 0 doesn't change the value,so remove it from the expression
4x=5
Divide both sides
44x=45
Divide the numbers
x=45
x=45,x−3≥0,x≥0x−3−2+3(−x)=0,x−3≥0,x<0−(x−3)−2+3x=0,x−3<0,x≥0−(x−3)−2+3(−x)=0,x−3<0,x<0
Solve the inequality
More Steps
Evaluate
x−3≥0
Move the constant to the right side
x≥0+3
Removing 0 doesn't change the value,so remove it from the expression
x≥3
x=45,x≥3,x≥0x−3−2+3(−x)=0,x−3≥0,x<0−(x−3)−2+3x=0,x−3<0,x≥0−(x−3)−2+3(−x)=0,x−3<0,x<0
Solve the equation
More Steps
Evaluate
x−3−2+3(−x)=0
Calculate the sum or difference
More Steps
Evaluate
x−3−2+3(−x)
Rewrite the expression
x−3−2−3x
Subtract the terms
−2x−3−2
Subtract the numbers
−2x−5
−2x−5=0
Move the constant to the right-hand side and change its sign
−2x=0+5
Removing 0 doesn't change the value,so remove it from the expression
−2x=5
Change the signs on both sides of the equation
2x=−5
Divide both sides
22x=2−5
Divide the numbers
x=2−5
Use b−a=−ba=−ba to rewrite the fraction
x=−25
x=45,x≥3,x≥0x=−25,x−3≥0,x<0−(x−3)−2+3x=0,x−3<0,x≥0−(x−3)−2+3(−x)=0,x−3<0,x<0
Solve the inequality
More Steps
Evaluate
x−3≥0
Move the constant to the right side
x≥0+3
Removing 0 doesn't change the value,so remove it from the expression
x≥3
x=45,x≥3,x≥0x=−25,x≥3,x<0−(x−3)−2+3x=0,x−3<0,x≥0−(x−3)−2+3(−x)=0,x−3<0,x<0
Solve the equation
More Steps
Evaluate
−(x−3)−2+3x=0
Calculate
−x+3−2+3x=0
Calculate the sum or difference
More Steps
Evaluate
−x+3−2+3x
Add the terms
2x+3−2
Subtract the numbers
2x+1
2x+1=0
Move the constant to the right-hand side and change its sign
2x=0−1
Removing 0 doesn't change the value,so remove it from the expression
2x=−1
Divide both sides
22x=2−1
Divide the numbers
x=2−1
Use b−a=−ba=−ba to rewrite the fraction
x=−21
x=45,x≥3,x≥0x=−25,x≥3,x<0x=−21,x−3<0,x≥0−(x−3)−2+3(−x)=0,x−3<0,x<0
Solve the inequality
More Steps
Evaluate
x−3<0
Move the constant to the right side
x<0+3
Removing 0 doesn't change the value,so remove it from the expression
x<3
x=45,x≥3,x≥0x=−25,x≥3,x<0x=−21,x<3,x≥0−(x−3)−2+3(−x)=0,x−3<0,x<0
Solve the equation
More Steps
Evaluate
−(x−3)−2+3(−x)=0
Calculate
−x+3−2+3(−x)=0
Calculate the sum or difference
More Steps
Evaluate
−x+3−2+3(−x)
Rewrite the expression
−x+3−2−3x
Subtract the terms
−4x+3−2
Subtract the numbers
−4x+1
−4x+1=0
Move the constant to the right-hand side and change its sign
−4x=0−1
Removing 0 doesn't change the value,so remove it from the expression
−4x=−1
Change the signs on both sides of the equation
4x=1
Divide both sides
44x=41
Divide the numbers
x=41
x=45,x≥3,x≥0x=−25,x≥3,x<0x=−21,x<3,x≥0x=41,x−3<0,x<0
Solve the inequality
More Steps
Evaluate
x−3<0
Move the constant to the right side
x<0+3
Removing 0 doesn't change the value,so remove it from the expression
x<3
x=45,x≥3,x≥0x=−25,x≥3,x<0x=−21,x<3,x≥0x=41,x<3,x<0
Find the intersection
x∈∅x=−25,x≥3,x<0x=−21,x<3,x≥0x=41,x<3,x<0
Find the intersection
x∈∅x∈∅x=−21,x<3,x≥0x=41,x<3,x<0
Find the intersection
x∈∅x∈∅x∈∅x=41,x<3,x<0
Find the intersection
x∈∅x∈∅x∈∅x∈∅
Solution
x∈∅
Alternative Form
No solution
Show Solution
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