Identify Equation: Identify the equation to solve for x. The equation given is 3−5+6x−1=x−6.
Find Common Denominator: Find a common denominator for the fractions on the left side of the equation.The common denominator for 3 and 6 is 6. We will multiply the terms by the appropriate factors to get rid of the denominators.
Multiply by Common Denominator: Multiply the entire equation by the common denominator to clear the fractions.Multiplying each term by 6 gives us:6×3−5+6×6x−1=6×(x−6)
Simplify Equation: Simplify the equation.Simplifying each term, we get:−10+(x−1)=6x−36
Distribute and Combine: Distribute and combine like terms.We will distribute the 6 on the right side and combine like terms:−10+x−1=6x−36
Simplify Left Side: Simplify the left side of the equation.Combining −10 and −1, we get:x−11=6x−36
Move Terms: Move the x terms to one side and the constant terms to the other side.Subtract x from both sides and add 36 to both sides:x−11−x=6x−36−x36−11=6x−x−36+36
Simplify Both Sides: Simplify both sides of the equation. 25=5x
Solve for x: Solve for x.Divide both sides by 5 to isolate x:525=55xx=5