What is the slope of this line whose equation is y=1/6x

     

This solution deals with adding, subtracting & finding the least common multiple.




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Step by Step Solution

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Rearrange:

Rearrange the equation by subtracting what is lớn the right of the equal sign from both sides of the equation : 1/6*x-1/2-(1/3*x+2/3)=0

Step by step solution :

Step 1 :

2 Simplify — 3Equation at the kết thúc of step 1 : 1 1 1 2 ((—•x)-—)-((—•x)+—) = 0 6 2 3 3

Step 2 :

1 Simplify — 3Equation at the kết thúc of step 2 : 1 1 1 2 ((—•x)-—)-((—•x)+—) = 0 6 2 3 3

Step 3 :

Adding fractions which have a common denominator :3.1 Adding fractions which have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce lớn lowest terms if possible:

x + 2 x + 2 ————— = ————— 3 3 Equation at the kết thúc of step 3 : 1 1 (x + 2) ((— • x) - —) - ——————— = 0 6 2 3

Step 4 :

1 Simplify — 2Equation at the over of step 4 : 1 1 (x + 2) ((— • x) - —) - ——————— = 0 6 2 3

Step 5 :

1 Simplify — 6Equation at the over of step 5 : 1 1 (x + 2) ((— • x) - —) - ——————— = 0 6 2 3

Step 6 :

Calculating the Least Common Multiple :6.1 Find the Least Common Multiple The left denominator is : 6 The right denominator is : 2

Number of times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
2111
3101
Product of allPrime Factors626

Least Common Multiple: 6

Calculating Multipliers :

6.2 Calculate multipliers for the two fractions Denote the Least Common Multiple by L.C.M Denote the Left Multiplier by Left_M Denote the Right Multiplier by Right_M Denote the Left Deniminator by L_Deno Denote the Right Multiplier by R_DenoLeft_M=L.C.M/L_Deno=1Right_M=L.C.M/R_Deno=3

Making Equivalent Fractions :

6.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. X —————————————————— = — L.C.M 6 R. Mult. • R. Num.

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3 —————————————————— = — L.C.M 6Adding fractions that have a common denominator :6.4 Adding up the two equivalent fractions showroom the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce lớn lowest terms if possible:

x - (3) x - 3 ——————— = ————— 6 6 Equation at the end of step 6 : (x - 3) (x + 2) ——————— - ——————— = 0 6 3

Step 7 :

Calculating the Least Common Multiple :7.1 Find the Least Common Multiple The left denominator is : 6 The right denominator is : 3

Number of times each prime factorappears in the factorization of:PrimeFactorLeftDenominatorRightDenominatorL.C.M = MaxLeft,Right
2101
3111
Product of allPrime Factors636

Least Common Multiple: 6

Calculating Multipliers :

7.2 Calculate multipliers for the two fractions Denote the Least Common Multiple by L.C.M Denote the Left Multiplier by Left_M Denote the Right Multiplier by Right_M Denote the Left Deniminator by L_Deno Denote the Right Multiplier by R_DenoLeft_M=L.C.M/L_Deno=1Right_M=L.C.M/R_Deno=2

Making Equivalent Fractions :

7.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. (x-3) —————————————————— = ————— L.C.M 6 R. Mult. • R. Num. (x+2) • 2 —————————————————— = ————————— L.C.M 6 Adding fractions that have a common denominator :7.4 Adding up the two equivalent fractions

(x-3) - ((x+2) • 2) -x - 7 ——————————————————— = —————— 6 6

Step 8 :

Pulling out lượt thích terms :8.1 Pull out lượt thích factors:-x - 7=-1•(x + 7)

Equation at the kết thúc of step 8 : -x - 7 —————— = 0 6

Step 9 :

When a fraction equals zero :9.1 When a fraction equals zero ...Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.Here"s how:

-x-7 ———— • 6 = 0 • 6 6 Now, on the left hand side, the 6 cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape:-x-7=0

Solving a Single Variable Equation:9.2Solve:-x-7 = 0Add 7 khổng lồ both sides of the equation:-x = 7 Multiply both sides of the equation by (-1) : x = -7