Question

how to solve for x
8-7|3x-2|=-20

Answer 1

there are two conditions for this

(I)when 3x-2>0 i.e. x>2/3

then the equation becomes 8-7(3x-2)=-20

(II) when 3x-2<0 i.e. x<2/3;

then the equation becomes 8-7(-3x+2)=-20

solve both of them.

Answer 2

Step 1 :

7
Simplify x - —
8
Rewriting the whole as an Equivalent Fraction :

1.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 8 as the denominator :

x x • 8
x = — = ———————————————
1 8
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

1.2 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:

x • 8 - (7) 8x - 7
——————————— = ——————
8 8
Equation at the end of step 1 :

(8x - 7) 7
———————— - — = 0
8 2
Step 2 :

8x-7 7
Simplify ———— - —
8 2
Calculating the Least Common Multiplier :

2.1 Find the Least Common Multiple

The left denominator is :
8

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}
2 3 1 3
Product of all
Prime Factors 8 2 8

Least Common Multiple:
8

Calculating Multipliers :

2.2 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 = 4


Making Equivalent Fractions :

2.3 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. (8x-7)
—————————————————— = ——————
L.C.M 8

R. Mult. • R. Num. 7 • 4
—————————————————— = —————
L.C.M 8
Adding fractions that have a common denominator :

2.4 Adding up the two equivalent fractions


(8x-7) - (7 • 4) 8x - 35
———————————————— = ———————
8 8
Equation at the end of step 2 :

8x - 35
——————— = 0
8
Step 3 :

8x-35
Solve ————— = 0
8
When a fraction equals zero :

3.1 When a fraction equals zero ...
Where a fraction equals zero, its nominator, 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:

8x-35
————— • 8 = 0 • 8
8
Now, on the left hand side, the 8 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
8x-35 = 0

Solving a Single Variable Equation :

3.2 Solve : 8x-35 = 0

Add 35 to both sides of the equation :
8x = 35
Divide both sides of the equation by 8:
x = 35/8
One solution was found :

x = 35/8