Solving a Single Variable Equation :
<span> 2.3 </span> Solve : <span> 3v-5 = 0</span><span>
</span>Add <span> 5</span> to both sides of the equation :<span>
</span> <span> 3v = 5</span>
Divide both sides of the equation by 3:
<span> v = 5/3 = 1.667</span>
One solution was found :<span> </span><span> v = 5/3 = 1.667</span>
Making Equivalent Fractions :<span><span> 1.3 </span> Rewrite the two fractions into<span> equivalent fractions</span>
Two fractions are called <span>equivalent </span>if they have the<span> same numeric value.</span>
For example : 1/2 and 2/4 are equivalent, <span> y/(y+1)2 </span> and <span> (y2+y)/(y+1)3 </span>are equivalent as well.
To calculate equivalent fraction , multiply the <span>Numerator </span>of each fraction, by its respectiveMultiplier.</span><span> L. Mult. • L. Num. 5v • 3
—————————————————— = ——————
L.C.M 39
R. Mult. • R. Num. 25
—————————————————— = —— </span> L.C.M 39Calculating the Least Common Multiple :<span><span> 1.1 </span> Find the Least Common Multiple
The left denominator is : <span> 13 </span>
The right denominator is : <span> 39 </span>
</span><span><span> Number of times each prime factor
appears in the factorization of:</span><span><span><span> Prime
Factor </span><span> Left
Denominator </span><span> Right
Denominator </span><span> L.C.M = Max
{Left,Right} </span></span><span>13111</span><span>3011</span><span><span> Product of all
Prime Factors </span>133939</span></span></span><span>
Least Common Multiple:
</span> 39 <span>v = 5/3 = 1.667 next
rearrange = </span><span>5*v/13-(25/39)=0
</span>Step by step solution:part 1: 5v 25 Simplify —— - —— 13 39
Calculating Multipliers :<span><span> 1.2 </span> 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_Deno
Left_M = L.C.M / L_Deno = 3
<span>Right_M = L.C.M / R_Deno = 1
</span>
</span>Pulling out like terms :<span><span> 1.5 </span> Pull out like factors :
15v - 25 = 5 • (3v - 5)
</span><span>Equation at the end of step 1 :</span> 5 • (3v - 5)
———————————— = 0
39
Step 2 :<span> 5•(3v-5)
Solve ———————— = 0
39
</span><span>
</span>