Solve completely 2/3(x+1 1/5)

# Why Should We Clear Fractions When Solving Linear Equations And Inequalities? Demonstrate How This Is Done With An Example.

Clearing fractions generally simplifies the problem by removing the necessity to do arithmetic with fractions. If you are comfortable with that arithmetic, some steps can be saved.

__Example__2/3(x + 1 1/5) < 4/7 The least common denominator of the fractions is 3*5*7=105, so we can clear them all by multiplying by this value. It may be less confusing to use the distributive property first. (2/3)x + (2/3)(6/5) < 4/7 70x + 84 < 60 (multiply the above equation by 105. The fractions are gone.) 70x < -24 (subtract 84) x < -24/70 (divide by 70) x < -12/35 (reduce the result) If we work the problem directly, we have (x + 1 1/5) < (3/2)*(4/7) (multiply both sides by 3/2) x < 6/7 - 6/5 (subtract 1 1/5 from both sides) x < (30 - 42)/35 (compute the difference of the two fractions) x < -12/35 (simplify)