Solve 7(1)/(2)\div6(2)/(5)=5(5)/(8)\divx

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Question

$$7 \frac{ 1 }{ 2 } \div 6 \frac{ 2 }{ 5 } =5 \frac{ 5 }{ 8 } \div x$$

Solve for x

$x = \frac{24}{5} = 4\frac{4}{5} = 4.8$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $x$.

$$\frac{5}{32}x\times \frac{7\times 2+1}{2}=\frac{5\times 8+5}{8}$$

Multiply $7$ and $2$ to get $14$.

$$\frac{5}{32}x\times \frac{14+1}{2}=\frac{5\times 8+5}{8}$$

Add $14$ and $1$ to get $15$.

$$\frac{5}{32}x\times \frac{15}{2}=\frac{5\times 8+5}{8}$$

Multiply $\frac{5}{32}$ times $\frac{15}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 15}{32\times 2}x=\frac{5\times 8+5}{8}$$

Do the multiplications in the fraction $\frac{5\times 15}{32\times 2}$.

$$\frac{75}{64}x=\frac{5\times 8+5}{8}$$

Multiply $5$ and $8$ to get $40$.

$$\frac{75}{64}x=\frac{40+5}{8}$$

Add $40$ and $5$ to get $45$.

$$\frac{75}{64}x=\frac{45}{8}$$

Multiply both sides by $\frac{64}{75}$, the reciprocal of $\frac{75}{64}$.

$$x=\frac{45}{8}\times \frac{64}{75}$$

Multiply $\frac{45}{8}$ times $\frac{64}{75}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{45\times 64}{8\times 75}$$

Do the multiplications in the fraction $\frac{45\times 64}{8\times 75}$.

$$x=\frac{2880}{600}$$

Reduce the fraction $\frac{2880}{600}$ to lowest terms by extracting and canceling out $120$.

$$x=\frac{24}{5}$$

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