Solve for `x (7x+14)/(3)-(17-3x)/(5)=6x-(4x+2)/(3)-5 `
Answers
Answer:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
7*x+14/3-17-3*x/5-(6*x-4*x+2/3-5)=0
Step by step solution :
STEP
1
:
2
Simplify —
3
Equation at the end of step
1
:
14 x 2
(((7x+——)-17)-(3•—))-((2x+—)-5) = 0
3 5 3
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
2x 2x • 3
2x = —— = ——————
1 3
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 :
2.2 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:
2x • 3 + 2 6x + 2
—————————— = ——————
3 3
Equation at the end of step
2
:
14 x (6x+2)
(((7x+——)-17)-(3•—))-(——————-5) = 0
3 5 3
STEP
3
:
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
5 5 • 3
5 = — = —————
1 3
STEP
4
:
Pulling out like terms :
4.1 Pull out like factors :
6x + 2 = 2 • (3x + 1)
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
2 • (3x+1) - (5 • 3) 6x - 13
———————————————————— = ———————
3 3
Equation at the end of step
4
:
14 x (6x-13)
(((7x+——)-17)-(3•—))-——————— = 0
3 5 3
STEP
5
:
x
Simplify —
5
Equation at the end of step
5
:
14 x (6x-13)
(((7x+——)-17)-(3•—))-——————— = 0
3 5 3
STEP
6
:
14
Simplify ——
3
Equation at the end of step
6
:
14 3x (6x - 13)
(((7x + ——) - 17) - ——) - ————————— = 0
3 5 3
STEP
7
:
Rewriting the whole as an Equivalent Fraction :
7.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
7x 7x • 3
7x = —— = ——————
1 3
Adding fractions that have a common denominator :
7.2 Adding up the two equivalent fractions
7x • 3 + 14 21x + 14
——————————— = ————————
3 3
Equation at the end of step
7
:
(21x + 14) 3x (6x - 13)
((—————————— - 17) - ——) - ————————— = 0
3 5 3
STEP
8
:
Rewriting the whole as an Equivalent Fraction :
8.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
17 17 • 3
17 = —— = ——————
1 3
STEP
9
:
Pulling out like terms :
9.1 Pull out like factors :
21x + 14 = 7 • (3x + 2)
Adding fractions that have a common denominator :
9.2 Adding up the two equivalent fractions
7 • (3x+2) - (17 • 3) 21x - 37
————————————————————— = ————————
3 3
Equation at the end of step
9
:
(21x - 37) 3x (6x - 13)
(—————————— - ——) - ————————— = 0
3 5 3
STEP
10
:
Calculating the Least Common Multiple :
10.1 Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 5