Solve (-18x+13y-35/48z^2)-(5/2x-z^2+11y)+(5/48z^2+15/2x)

$$( - 18 x + 13 y - \frac { 35 } { 48 } z ^ { 2 } ) - ( \frac { 5 } { 2 } x - z ^ { 2 } + 11 y ) + ( \frac { 5 } { 48 } z ^ { 2 } + \frac { 15 } { 2 } x )$$

Evaluate

$$\frac{3z^{2}}{8}+2y-13x$$

Solution Steps

To find the opposite of \frac{5}{2}x-z^{2}+11y, find the opposite of each term.

$$-18x+13y-\frac{35}{48}z^{2}-\frac{5}{2}x+z^{2}-11y+\frac{5}{48}z^{2}+\frac{15}{2}x$$

Combine -18x and -\frac{5}{2}x to get -\frac{41}{2}x.

$$-\frac{41}{2}x+13y-\frac{35}{48}z^{2}+z^{2}-11y+\frac{5}{48}z^{2}+\frac{15}{2}x$$

Combine -\frac{35}{48}z^{2} and z^{2} to get \frac{13}{48}z^{2}.

$$-\frac{41}{2}x+13y+\frac{13}{48}z^{2}-11y+\frac{5}{48}z^{2}+\frac{15}{2}x$$

Combine 13y and -11y to get 2y.

$$-\frac{41}{2}x+2y+\frac{13}{48}z^{2}+\frac{5}{48}z^{2}+\frac{15}{2}x$$

Combine \frac{13}{48}z^{2} and \frac{5}{48}z^{2} to get \frac{3}{8}z^{2}.

$$-\frac{41}{2}x+2y+\frac{3}{8}z^{2}+\frac{15}{2}x$$

Combine -\frac{41}{2}x and \frac{15}{2}x to get -13x.

$$-13x+2y+\frac{3}{8}z^{2}$$

Expand

$$\frac{3z^{2}}{8}+2y-13x$$

Solution Steps

To find the opposite of \frac{5}{2}x-z^{2}+11y, find the opposite of each term.

$$-18x+13y-\frac{35}{48}z^{2}-\frac{5}{2}x+z^{2}-11y+\frac{5}{48}z^{2}+\frac{15}{2}x$$

Combine -18x and -\frac{5}{2}x to get -\frac{41}{2}x.

$$-\frac{41}{2}x+13y-\frac{35}{48}z^{2}+z^{2}-11y+\frac{5}{48}z^{2}+\frac{15}{2}x$$

Combine -\frac{35}{48}z^{2} and z^{2} to get \frac{13}{48}z^{2}.

$$-\frac{41}{2}x+13y+\frac{13}{48}z^{2}-11y+\frac{5}{48}z^{2}+\frac{15}{2}x$$

Combine 13y and -11y to get 2y.

$$-\frac{41}{2}x+2y+\frac{13}{48}z^{2}+\frac{5}{48}z^{2}+\frac{15}{2}x$$

Combine \frac{13}{48}z^{2} and \frac{5}{48}z^{2} to get \frac{3}{8}z^{2}.

$$-\frac{41}{2}x+2y+\frac{3}{8}z^{2}+\frac{15}{2}x$$

Combine -\frac{41}{2}x and \frac{15}{2}x to get -13x.

$$-13x+2y+\frac{3}{8}z^{2}$$