Solve for a
a=7
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144-24\left(\frac{2a+1}{3}-\frac{1-3a}{4}\right)=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Multiply both sides of the equation by 24, the least common multiple of 3,4,8.
144-24\left(\frac{4\left(2a+1\right)}{12}-\frac{3\left(1-3a\right)}{12}\right)=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 4 is 12. Multiply \frac{2a+1}{3} times \frac{4}{4}. Multiply \frac{1-3a}{4} times \frac{3}{3}.
144-24\times \frac{4\left(2a+1\right)-3\left(1-3a\right)}{12}=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Since \frac{4\left(2a+1\right)}{12} and \frac{3\left(1-3a\right)}{12} have the same denominator, subtract them by subtracting their numerators.
144-24\times \frac{8a+4-3+9a}{12}=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Do the multiplications in 4\left(2a+1\right)-3\left(1-3a\right).
144-24\times \frac{17a+1}{12}=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Combine like terms in 8a+4-3+9a.
144-2\left(17a+1\right)=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Cancel out 12, the greatest common factor in 24 and 12.
144-34a-2=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Use the distributive property to multiply -2 by 17a+1.
142-34a=120-24\left(\frac{7a-1}{8}-\frac{5-2a}{3}\right)
Subtract 2 from 144 to get 142.
142-34a=120-24\left(\frac{3\left(7a-1\right)}{24}-\frac{8\left(5-2a\right)}{24}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 3 is 24. Multiply \frac{7a-1}{8} times \frac{3}{3}. Multiply \frac{5-2a}{3} times \frac{8}{8}.
142-34a=120-24\times \frac{3\left(7a-1\right)-8\left(5-2a\right)}{24}
Since \frac{3\left(7a-1\right)}{24} and \frac{8\left(5-2a\right)}{24} have the same denominator, subtract them by subtracting their numerators.
142-34a=120-24\times \frac{21a-3-40+16a}{24}
Do the multiplications in 3\left(7a-1\right)-8\left(5-2a\right).
142-34a=120-24\times \frac{37a-43}{24}
Combine like terms in 21a-3-40+16a.
142-34a=120-\frac{24\left(37a-43\right)}{24}
Express 24\times \frac{37a-43}{24} as a single fraction.
142-34a=120-\left(37a-43\right)
Cancel out 24 and 24.
142-34a=120-37a-\left(-43\right)
To find the opposite of 37a-43, find the opposite of each term.
142-34a=120-37a+43
The opposite of -43 is 43.
142-34a=163-37a
Add 120 and 43 to get 163.
142-34a+37a=163
Add 37a to both sides.
142+3a=163
Combine -34a and 37a to get 3a.
3a=163-142
Subtract 142 from both sides.
3a=21
Subtract 142 from 163 to get 21.
a=\frac{21}{3}
Divide both sides by 3.
a=7
Divide 21 by 3 to get 7.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}