Solve 5+3(a+4)=7a-(9-10a)+4

$$5 + 3 ( a + 4 ) = 7 a - ( 9 - 10 a ) + 4$$

Solve for a

$$a = \frac{11}{7} = 1\frac{4}{7} \approx 1.571428571$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by a+4.

$$5+3a+12=7a-\left(9-10a\right)+4$$

Add 5 and 12 to get 17.

$$17+3a=7a-\left(9-10a\right)+4$$

To find the opposite of 9-10a, find the opposite of each term.

$$17+3a=7a-9-\left(-10a\right)+4$$

The opposite of -10a is 10a.

$$17+3a=7a-9+10a+4$$

Combine 7a and 10a to get 17a.

$$17+3a=17a-9+4$$

Add -9 and 4 to get -5.

$$17+3a=17a-5$$

Subtract 17a from both sides.

$$17+3a-17a=-5$$

Combine 3a and -17a to get -14a.

$$17-14a=-5$$

Subtract 17 from both sides.

$$-14a=-5-17$$

Subtract 17 from -5 to get -22.

$$-14a=-22$$

Divide both sides by -14.

$$a=\frac{-22}{-14}$$

Reduce the fraction \frac{-22}{-14} to lowest terms by extracting and canceling out -2.

$$a=\frac{11}{7}$$