Solve (21/10-x)div8+12/15=11/3

$$( 2 \frac { 1 } { 10 } -x) \div 8+ 1 \frac { 2 } { 15 } = 1 \frac { 1 } { 3 }$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 120, the least common multiple of 8,15,3.

$$15\left(\frac{2\times 10+1}{10}-x\right)+8\left(1\times 15+2\right)=40\left(1\times 3+1\right)$$

Multiply 2 and 10 to get 20.

$$15\left(\frac{20+1}{10}-x\right)+8\left(1\times 15+2\right)=40\left(1\times 3+1\right)$$

Add 20 and 1 to get 21.

$$15\left(\frac{21}{10}-x\right)+8\left(1\times 15+2\right)=40\left(1\times 3+1\right)$$

Use the distributive property to multiply 15 by \frac{21}{10}-x.

$$15\times \frac{21}{10}-15x+8\left(1\times 15+2\right)=40\left(1\times 3+1\right)$$

Express 15\times \frac{21}{10} as a single fraction.

$$\frac{15\times 21}{10}-15x+8\left(1\times 15+2\right)=40\left(1\times 3+1\right)$$

Multiply 15 and 21 to get 315.

$$\frac{315}{10}-15x+8\left(1\times 15+2\right)=40\left(1\times 3+1\right)$$

Reduce the fraction \frac{315}{10} to lowest terms by extracting and canceling out 5.

$$\frac{63}{2}-15x+8\left(1\times 15+2\right)=40\left(1\times 3+1\right)$$

Multiply 1 and 15 to get 15.

$$\frac{63}{2}-15x+8\left(15+2\right)=40\left(1\times 3+1\right)$$

Add 15 and 2 to get 17.

$$\frac{63}{2}-15x+8\times 17=40\left(1\times 3+1\right)$$

Multiply 8 and 17 to get 136.

$$\frac{63}{2}-15x+136=40\left(1\times 3+1\right)$$

Convert 136 to fraction \frac{272}{2}.

$$\frac{63}{2}-15x+\frac{272}{2}=40\left(1\times 3+1\right)$$

Since \frac{63}{2} and \frac{272}{2} have the same denominator, add them by adding their numerators.

$$\frac{63+272}{2}-15x=40\left(1\times 3+1\right)$$

Add 63 and 272 to get 335.

$$\frac{335}{2}-15x=40\left(1\times 3+1\right)$$

Multiply 1 and 3 to get 3.

$$\frac{335}{2}-15x=40\left(3+1\right)$$

Add 3 and 1 to get 4.

$$\frac{335}{2}-15x=40\times 4$$

Multiply 40 and 4 to get 160.

$$\frac{335}{2}-15x=160$$

Subtract \frac{335}{2} from both sides.

$$-15x=160-\frac{335}{2}$$

Convert 160 to fraction \frac{320}{2}.

$$-15x=\frac{320}{2}-\frac{335}{2}$$

Since \frac{320}{2} and \frac{335}{2} have the same denominator, subtract them by subtracting their numerators.

$$-15x=\frac{320-335}{2}$$

Subtract 335 from 320 to get -15.

$$-15x=-\frac{15}{2}$$

Divide both sides by -15.

$$x=\frac{-\frac{15}{2}}{-15}$$

Express \frac{-\frac{15}{2}}{-15} as a single fraction.

$$x=\frac{-15}{2\left(-15\right)}$$

Cancel out -15 in both numerator and denominator.

$$x=\frac{1}{2}$$