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Question
\frac{5}{2}\left(x-2\right)=\frac{3}{4}x-1-\frac{1}{4}x
Solve the equation
x=2
Evaluate
\frac{5}{2}\left(x-2\right)=\frac{3}{4}x-1-\frac{1}{4}x
Multiply the terms
More Steps
Evaluate
\frac{5}{2}\left(x-2\right)
Apply the distributive property
\frac{5}{2}x-\frac{5}{2}\times 2
Multiply the numbers
More Steps
Evaluate
\frac{5}{2}\times 2
Reduce the numbers
5\times 1
Simplify
5
\frac{5}{2}x-5
\frac{5}{2}x-5=\frac{3}{4}x-1-\frac{1}{4}x
Subtract the terms
More Steps
Evaluate
\frac{3}{4}x-\frac{1}{4}x
Collect like terms by calculating the sum or difference of their coefficients
\left(\frac{3}{4}-\frac{1}{4}\right)x
Subtract the numbers
More Steps
Evaluate
\frac{3}{4}-\frac{1}{4}
Write all numerators above the common denominator
\frac{3-1}{4}
Subtract the numbers
\frac{2}{4}
\text{Cancel out the common factor }2
\frac{1}{2}
\frac{1}{2}x
\frac{5}{2}x-5=\frac{1}{2}x-1
Multiply both sides of the equation by LCM
\left(\frac{5}{2}x-5\right)\times 2=\left(\frac{1}{2}x-1\right)\times 2
Calculate
More Steps
Evaluate
\left(\frac{5}{2}x-5\right)\times 2
Apply the distributive property
\frac{5}{2}x\times 2-5\times 2
Multiply the numbers
More Steps
Evaluate
\frac{5}{2}\times 2
Reduce the numbers
5\times 1
Simplify
5
5x-5\times 2
Multiply the numbers
5x-10
5x-10=\left(\frac{1}{2}x-1\right)\times 2
Calculate
More Steps
Evaluate
\left(\frac{1}{2}x-1\right)\times 2
Apply the distributive property
\frac{1}{2}x\times 2-2
Multiply the numbers
More Steps
Evaluate
\frac{1}{2}\times 2
Reduce the numbers
1\times 1
Simplify
1
x-2
5x-10=x-2
Move the expression to the left side
5x-10-x=-2
Move the expression to the right side
5x-x=-2+10
Add and subtract
More Steps
Evaluate
5x-x
Collect like terms by calculating the sum or difference of their coefficients
\left(5-1\right)x
Subtract the numbers
4x
4x=-2+10
Add and subtract
4x=8
Divide both sides
\frac{4x}{4}=\frac{8}{4}
Divide the numbers
x=\frac{8}{4}
Solution
More Steps
Evaluate
\frac{8}{4}
Reduce the numbers
\frac{2}{1}
Calculate
2
x=2
Show Solutions
Rewrite the equation
x=2
Evaluate
\frac{5}{2}\left(x-2\right)=\frac{3}{4}x-1-\frac{1}{4}x
Evaluate
More Steps
Evaluate
\frac{5}{2}\left(x-2\right)
Apply the distributive property
\frac{5}{2}x-\frac{5}{2}\times 2
Multiply the numbers
More Steps
Evaluate
\frac{5}{2}\times 2
Reduce the numbers
5\times 1
Simplify
5
\frac{5}{2}x-5
\frac{5}{2}x-5=\frac{3}{4}x-1-\frac{1}{4}x
Evaluate
More Steps
Evaluate
\frac{3}{4}x-1-\frac{1}{4}x
Subtract the terms
More Steps
Evaluate
\frac{3}{4}x-\frac{1}{4}x
Collect like terms by calculating the sum or difference of their coefficients
\left(\frac{3}{4}-\frac{1}{4}\right)x
Subtract the numbers
\frac{1}{2}x
\frac{1}{2}x-1
\frac{5}{2}x-5=\frac{1}{2}x-1
Multiply both sides of the equation by LCD
5x-10=x-2
Move the variable to the left side
4x-10=-2
Move the constant to the right side
4x=8
Solution
x=2
Show Solutions
Graph
