Solve 43/10-(22/5x+51/2)=1/2(-3frac{3}{5}x+1frac{1}{5})?

$$4 \frac { 3 } { 10 } - ( 2 \frac { 2 } { 5 } x + 5 \frac { 1 } { 2 } ) = \frac { 1 } { 2 } ( - 3 \frac { 3 } { 5 } x + 1 \frac { 1 } { 5 } ) ?$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 10,5,2.

$$4\times 10+3-10\left(\frac{2\times 5+2}{5}x+\frac{5\times 2+1}{2}\right)=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Multiply 4 and 10 to get 40.

$$40+3-10\left(\frac{2\times 5+2}{5}x+\frac{5\times 2+1}{2}\right)=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Add 40 and 3 to get 43.

$$43-10\left(\frac{2\times 5+2}{5}x+\frac{5\times 2+1}{2}\right)=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Multiply 2 and 5 to get 10.

$$43-10\left(\frac{10+2}{5}x+\frac{5\times 2+1}{2}\right)=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Add 10 and 2 to get 12.

$$43-10\left(\frac{12}{5}x+\frac{5\times 2+1}{2}\right)=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Multiply 5 and 2 to get 10.

$$43-10\left(\frac{12}{5}x+\frac{10+1}{2}\right)=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Add 10 and 1 to get 11.

$$43-10\left(\frac{12}{5}x+\frac{11}{2}\right)=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Use the distributive property to multiply -10 by \frac{12}{5}x+\frac{11}{2}.

$$43-10\times \frac{12}{5}x-10\times \frac{11}{2}=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Express -10\times \frac{12}{5} as a single fraction.

$$43+\frac{-10\times 12}{5}x-10\times \frac{11}{2}=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Multiply -10 and 12 to get -120.

$$43+\frac{-120}{5}x-10\times \frac{11}{2}=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Divide -120 by 5 to get -24.

$$43-24x-10\times \frac{11}{2}=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Express -10\times \frac{11}{2} as a single fraction.

$$43-24x+\frac{-10\times 11}{2}=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Multiply -10 and 11 to get -110.

$$43-24x+\frac{-110}{2}=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Divide -110 by 2 to get -55.

$$43-24x-55=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Subtract 55 from 43 to get -12.

$$-12-24x=5\left(\left(-\frac{3\times 5+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Multiply 3 and 5 to get 15.

$$-12-24x=5\left(\left(-\frac{15+3}{5}\right)x+\frac{1\times 5+1}{5}\right)$$

Add 15 and 3 to get 18.

$$-12-24x=5\left(-\frac{18}{5}x+\frac{1\times 5+1}{5}\right)$$

Multiply 1 and 5 to get 5.

$$-12-24x=5\left(-\frac{18}{5}x+\frac{5+1}{5}\right)$$

Add 5 and 1 to get 6.

$$-12-24x=5\left(-\frac{18}{5}x+\frac{6}{5}\right)$$

Use the distributive property to multiply 5 by -\frac{18}{5}x+\frac{6}{5}.

$$-12-24x=5\left(-\frac{18}{5}\right)x+5\times \frac{6}{5}$$

Cancel out 5 and 5.

$$-12-24x=-18x+5\times \frac{6}{5}$$

Cancel out 5 and 5.

$$-12-24x=-18x+6$$

Add 18x to both sides.

$$-12-24x+18x=6$$

Combine -24x and 18x to get -6x.

$$-12-6x=6$$

Add 12 to both sides.

$$-6x=6+12$$

Add 6 and 12 to get 18.

$$-6x=18$$

Divide both sides by -6.

$$x=\frac{18}{-6}$$

Divide 18 by -6 to get -3.

$$x=-3$$