Question
Solve the equation
x=353
Alternative Form
x=0.08˙57142˙
Evaluate
2∣9−2x∣=206x
Transform the expression
2(9−2x)=206x,9−2x≥02(−9+2x)=206x,9−2x<0
Calculate
More Steps

Calculate
2(9−2x)=206x
Expand the expression
More Steps

Evaluate
2(9−2x)
Apply the distributive property
2×9−2×2x
Multiply the numbers
18−2×2x
Multiply the numbers
18−4x
18−4x=206x
Move the variable to the left side
18−4x−206x=0
Subtract the terms
More Steps

Evaluate
−4x−206x
Collect like terms by calculating the sum or difference of their coefficients
(−4−206)x
Subtract the numbers
−210x
18−210x=0
Move the constant to the right side
−210x=0−18
Removing 0 doesn't change the value,so remove it from the expression
−210x=−18
Change the signs on both sides of the equation
210x=18
Divide both sides
210210x=21018
Divide the numbers
x=21018
Cancel out the common factor 6
x=353
x=353,9−2x≥02(−9+2x)=206x,9−2x<0
Calculate
More Steps

Calculate
9−2x≥0
Move the constant to the right side
−2x≥0−9
Removing 0 doesn't change the value,so remove it from the expression
−2x≥−9
Change the signs on both sides of the inequality and flip the inequality sign
2x≤9
Divide both sides
22x≤29
Divide the numbers
x≤29
x=353,x≤292(−9+2x)=206x,9−2x<0
Calculate
More Steps

Calculate
2(−9+2x)=206x
Expand the expression
More Steps

Evaluate
2(−9+2x)
Apply the distributive property
2(−9)+2×2x
Multiply the numbers
−18+2×2x
Multiply the numbers
−18+4x
−18+4x=206x
Move the variable to the left side
−18+4x−206x=0
Subtract the terms
More Steps

Evaluate
4x−206x
Collect like terms by calculating the sum or difference of their coefficients
(4−206)x
Subtract the numbers
−202x
−18−202x=0
Move the constant to the right side
−202x=0+18
Removing 0 doesn't change the value,so remove it from the expression
−202x=18
Change the signs on both sides of the equation
202x=−18
Divide both sides
202202x=202−18
Divide the numbers
x=202−18
Divide the numbers
More Steps

Evaluate
202−18
Cancel out the common factor 2
101−9
Use b−a=−ba=−ba to rewrite the fraction
−1019
x=−1019
x=353,x≤29x=−1019,9−2x<0
Calculate
More Steps

Calculate
9−2x<0
Move the constant to the right side
−2x<0−9
Removing 0 doesn't change the value,so remove it from the expression
−2x<−9
Change the signs on both sides of the inequality and flip the inequality sign
2x>9
Divide both sides
22x>29
Divide the numbers
x>29
x=353,x≤29x=−1019,x>29
Calculate
x=353x=−1019,x>29
Solution
x=353
Alternative Form
x=0.08˙57142˙
Show Solution
