Solve the linear equation step-by-step

Solving for x: three denominators: 4, 6, and 12.we can find the lcm of those denominatorswe can write each denominator as a product of prime factors    get the primes appearing the greatest number of times in any of the factors.we have unique factors of 2 and 3    highest power of 2 is 2²    highest power of 3 is 3the lcd you get from multiplying those highest powers of prime    lcd is 2²  · 3 = 12the point here is that we want all the fractions to have the same denominator. then we can multiply both sides of the equation by that denominator to cancel it out.    to make  have denominator of 12, we need to multiply the numerator and denominator by 2 (because 6  · 2 = 12):     to make  have a denominator of 12, we need to multiply the numerator and denominator by 3 (because 4  · 3 = 12):     multiply both sides of the entire equation by 12 so that it will cancel out all the denominators (distributes on the right-hand side)    10 and -12 sum up to get -2    get rid of x on left side by subtracting both sides by x.    add 2 to both sides    divide both sides by 2    answer is x = 9/2======checking our answer: plug in x = 9/2 into the original equation and see if we get a true statement.    multiplying the entire numerator and denominator of the fraction to get rid of the little denominators of "2"    the left-hand side has 24 in denominator; let us aim for thatget  to have a denominator of 24 by multiplying num and denom by 4 (because 6 (denominator)  · 4 = 24).get  to have a denominator of 24 by multiplying num and denom by 3 (because 8  · 3 = 24).    we get a true statement as 23/24 = 23/24.   

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