Solve 5*(0.5x+2.2)=16*(1/3x-29/32)

$$5 \times ( 0.5 x + 2.2 ) = 16 \times ( \frac { 1 } { 3 } x - \frac { 29 } { 32 } )$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 0.5x+2.2.

$$2.5x+11=16\left(\frac{1}{3}x-\frac{29}{32}\right)$$

Use the distributive property to multiply 16 by \frac{1}{3}x-\frac{29}{32}.

$$2.5x+11=16\times \frac{1}{3}x+16\left(-\frac{29}{32}\right)$$

Multiply 16 and \frac{1}{3} to get \frac{16}{3}.

$$2.5x+11=\frac{16}{3}x+16\left(-\frac{29}{32}\right)$$

Express 16\left(-\frac{29}{32}\right) as a single fraction.

$$2.5x+11=\frac{16}{3}x+\frac{16\left(-29\right)}{32}$$

Multiply 16 and -29 to get -464.

$$2.5x+11=\frac{16}{3}x+\frac{-464}{32}$$

Reduce the fraction \frac{-464}{32} to lowest terms by extracting and canceling out 16.

$$2.5x+11=\frac{16}{3}x-\frac{29}{2}$$

Subtract \frac{16}{3}x from both sides.

$$2.5x+11-\frac{16}{3}x=-\frac{29}{2}$$

Combine 2.5x and -\frac{16}{3}x to get -\frac{17}{6}x.

$$-\frac{17}{6}x+11=-\frac{29}{2}$$

Subtract 11 from both sides.

$$-\frac{17}{6}x=-\frac{29}{2}-11$$

Convert 11 to fraction \frac{22}{2}.

$$-\frac{17}{6}x=-\frac{29}{2}-\frac{22}{2}$$

Since -\frac{29}{2} and \frac{22}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{17}{6}x=\frac{-29-22}{2}$$

Subtract 22 from -29 to get -51.

$$-\frac{17}{6}x=-\frac{51}{2}$$

Multiply both sides by -\frac{6}{17}, the reciprocal of -\frac{17}{6}.

$$x=-\frac{51}{2}\left(-\frac{6}{17}\right)$$

Multiply -\frac{51}{2} times -\frac{6}{17} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-51\left(-6\right)}{2\times 17}$$

Do the multiplications in the fraction \frac{-51\left(-6\right)}{2\times 17}.

$$x=\frac{306}{34}$$

Divide 306 by 34 to get 9.

$$x=9$$