|2-5x|+3<10 how to solve

1 answer:

ivann1987 [24]3 years ago

4 0

1 Simplify — 2 Equation at the end of step 1 : 2 3 1 ((— • x) - ——) - — = 0 5 10 2 Step 2 : 3 Simplify —— 10 Equation at the end of step 2 : 2 3 1 ((— • x) - ——) - — = 0 5 10 2 Step 3 : 2 Simplify — 5 Equation at the end of step 3 : 2 3 1 ((— • x) - ——) - — = 0 5 10 2 Step 4 :Calculating the Least Common Multiple :

4.1 Find the Least Common Multiple

 The left denominator is : 5 

 The right denominator is : 10

Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} 51112011 Product of all
Prime Factors 51010

Least Common Multiple:
10

Calculating Multipliers :

4.2 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_Deno

 Left_M = L.C.M / L_Deno = 2

 Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

4.3 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 2x • 2 —————————————————— = —————— L.C.M 10 R. Mult. • R. Num. 3 —————————————————— = —— L.C.M 10 Adding fractions that have a common denominator :

4.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2x • 2 - (3) 4x - 3 ———————————— = —————— 10 10 Equation at the end of step 4 : (4x - 3) 1 ———————— - — = 0 10 2 Step 5 :Calculating the Least Common Multiple :

5.1 Find the Least Common Multiple

 The left denominator is : 10 

 The right denominator is : 2

Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} 21115101 Product of all
Prime Factors 10210

Least Common Multiple:
10

Calculating Multipliers :

5.2 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_Deno

 Left_M = L.C.M / L_Deno = 1

 Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

5.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. (4x-3) —————————————————— = —————— L.C.M 10 R. Mult. • R. Num. 5 —————————————————— = —— L.C.M 10 Adding fractions that have a common denominator :

5.4 Adding up the two equivalent fractions

(4x-3) - (5) 4x - 8 ———————————— = —————— 10 10 Step 6 :Pulling out like terms :

6.1 Pull out like factors :

4x - 8 = 4 • (x - 2)

Equation at the end of step 6 : 4 • (x - 2) ——————————— = 0 10 Step 7 :When a fraction equals zero : 7.1 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:

4•(x-2) ——————— • 10 = 0 • 10 10

Now, on the left hand side, the 10 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
4 • (x-2) = 0

Equations which are never true :

7.2 Solve : 4 = 0

This equation has no solution.
 A a non-zero constant never equals zero.

Solving a Single Variable Equation :

7.3 Solve : x-2 = 0

Add 2 to both sides of the equation :
 x = 2

One solution was found : x = 2