Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x≥7
Alternative Form
x∈[7,+∞)
Evaluate
∣x−7∣=x−7
Rewrite the expression
∣x−7∣−x+7=0
Separate the equation into 2 possible cases
x−7−x+7=0,x−7≥0−(x−7)−x+7=0,x−7<0
The statement is true for any value of x
More Steps
Evaluate
x−7−x+7=0
Calculate the sum or difference
More Steps
Evaluate
x−7−x+7
The sum of two opposites equals 0
0−7+7
Remove 0
−7+7
Add the numbers
0
0=0
The statement is true for any value of x
x∈R
x∈R,x−7≥0−(x−7)−x+7=0,x−7<0
Solve the inequality
More Steps
Evaluate
x−7≥0
Move the constant to the right side
x≥0+7
Removing 0 doesn't change the value,so remove it from the expression
x≥7
x∈R,x≥7−(x−7)−x+7=0,x−7<0
Solve the equation
More Steps
Evaluate
−(x−7)−x+7=0
Calculate
−x+7−x+7=0
Calculate the sum or difference
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Evaluate
−x+7−x+7
Subtract the terms
−2x+7+7
Add the numbers
−2x+14
−2x+14=0
Move the constant to the right-hand side and change its sign
−2x=0−14
Removing 0 doesn't change the value,so remove it from the expression
−2x=−14
Change the signs on both sides of the equation
2x=14
Divide both sides
22x=214
Divide the numbers
x=214
Divide the numbers
More Steps
Evaluate
214
Reduce the numbers
17
Calculate
7
x=7
x∈R,x≥7x=7,x−7<0
Solve the inequality
More Steps
Evaluate
x−7<0
Move the constant to the right side
x<0+7
Removing 0 doesn't change the value,so remove it from the expression
x<7
x∈R,x≥7x=7,x<7
Find the intersection
x≥7x=7,x<7
Find the intersection
x≥7x∈∅
Solution
x≥7
Alternative Form
x∈[7,+∞)
Show Solution
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