Solve 5 9 (7-6x)- 3 4 (3-15x) 1 12 (3x5)- 1 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{5}{9}(7-6x)-\frac{3}{4}(3-15x)\frac{1}{12}(3x5)-\frac{1}{2}$$

Evaluate

$\frac{45xx_{5}}{16}-\frac{9x_{5}}{16}-\frac{10x}{3}+\frac{61}{18}$

Solution Steps

Use the distributive property to multiply $\frac{5}{9}$ by $7-6x$.

$$\frac{5}{9}\times 7+\frac{5}{9}\left(-6\right)x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\times 3x_{5}-\frac{1}{2}$$

Express $\frac{5}{9}\times 7$ as a single fraction.

$$\frac{5\times 7}{9}+\frac{5}{9}\left(-6\right)x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\times 3x_{5}-\frac{1}{2}$$

Multiply $5$ and $7$ to get $35$.

$$\frac{35}{9}+\frac{5}{9}\left(-6\right)x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\times 3x_{5}-\frac{1}{2}$$

Express $\frac{5}{9}\left(-6\right)$ as a single fraction.

$$\frac{35}{9}+\frac{5\left(-6\right)}{9}x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\times 3x_{5}-\frac{1}{2}$$

Multiply $5$ and $-6$ to get $-30$.

$$\frac{35}{9}+\frac{-30}{9}x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\times 3x_{5}-\frac{1}{2}$$

Reduce the fraction $\frac{-30}{9}$ to lowest terms by extracting and canceling out $3$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\times 3x_{5}-\frac{1}{2}$$

Multiply $\frac{3}{4}$ times $\frac{1}{12}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3\times 1}{4\times 12}\left(3-15x\right)\times 3x_{5}-\frac{1}{2}$$

Do the multiplications in the fraction $\frac{3\times 1}{4\times 12}$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{48}\left(3-15x\right)\times 3x_{5}-\frac{1}{2}$$

Reduce the fraction $\frac{3}{48}$ to lowest terms by extracting and canceling out $3$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{1}{16}\left(3-15x\right)\times 3x_{5}-\frac{1}{2}$$

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

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{16}\left(3-15x\right)x_{5}-\frac{1}{2}$$

Use the distributive property to multiply $-\frac{3}{16}$ by $3-15x$.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{3}{16}\times 3-\frac{3}{16}\left(-15\right)x\right)x_{5}-\frac{1}{2}$$

Express $-\frac{3}{16}\times 3$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x+\left(\frac{-3\times 3}{16}-\frac{3}{16}\left(-15\right)x\right)x_{5}-\frac{1}{2}$$

Multiply $-3$ and $3$ to get $-9$.

$$\frac{35}{9}-\frac{10}{3}x+\left(\frac{-9}{16}-\frac{3}{16}\left(-15\right)x\right)x_{5}-\frac{1}{2}$$

Fraction $\frac{-9}{16}$ can be rewritten as $-\frac{9}{16}$ by extracting the negative sign.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{9}{16}-\frac{3}{16}\left(-15\right)x\right)x_{5}-\frac{1}{2}$$

Express $-\frac{3}{16}\left(-15\right)$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{9}{16}+\frac{-3\left(-15\right)}{16}x\right)x_{5}-\frac{1}{2}$$

Multiply $-3$ and $-15$ to get $45$.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{9}{16}+\frac{45}{16}x\right)x_{5}-\frac{1}{2}$$

Use the distributive property to multiply $-\frac{9}{16}+\frac{45}{16}x$ by $x_{5}$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x_{5}+\frac{45}{16}xx_{5}-\frac{1}{2}$$

Least common multiple of $9$ and $2$ is $18$. Convert $\frac{35}{9}$ and $\frac{1}{2}$ to fractions with denominator $18$.

$$\frac{70}{18}-\frac{10}{3}x-\frac{9}{16}x_{5}+\frac{45}{16}xx_{5}-\frac{9}{18}$$

Since $\frac{70}{18}$ and $\frac{9}{18}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{70-9}{18}-\frac{10}{3}x-\frac{9}{16}x_{5}+\frac{45}{16}xx_{5}$$

Subtract $9$ from $70$ to get $61$.

$$\frac{61}{18}-\frac{10}{3}x-\frac{9}{16}x_{5}+\frac{45}{16}xx_{5}$$

Expand

$\frac{45xx_{5}}{16}-\frac{9x_{5}}{16}-\frac{10x}{3}+\frac{61}{18}$

Solution Steps

Use the distributive property to multiply $\frac{5}{9}$ by $7-6x$.

$$\frac{5}{9}\times 7+\frac{5}{9}\left(-6\right)x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\times 3x_{5}-\frac{1}{2}$$

Express $\frac{5}{9}\times 7$ as a single fraction.

$$\frac{5\times 7}{9}+\frac{5}{9}\left(-6\right)x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\times 3x_{5}-\frac{1}{2}$$

Multiply $5$ and $7$ to get $35$.

$$\frac{35}{9}+\frac{5}{9}\left(-6\right)x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\times 3x_{5}-\frac{1}{2}$$

Express $\frac{5}{9}\left(-6\right)$ as a single fraction.

$$\frac{35}{9}+\frac{5\left(-6\right)}{9}x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\times 3x_{5}-\frac{1}{2}$$

Multiply $5$ and $-6$ to get $-30$.

$$\frac{35}{9}+\frac{-30}{9}x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\times 3x_{5}-\frac{1}{2}$$

Reduce the fraction $\frac{-30}{9}$ to lowest terms by extracting and canceling out $3$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{4}\left(3-15x\right)\times \frac{1}{12}\times 3x_{5}-\frac{1}{2}$$

Multiply $\frac{3}{4}$ times $\frac{1}{12}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3\times 1}{4\times 12}\left(3-15x\right)\times 3x_{5}-\frac{1}{2}$$

Do the multiplications in the fraction $\frac{3\times 1}{4\times 12}$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{48}\left(3-15x\right)\times 3x_{5}-\frac{1}{2}$$

Reduce the fraction $\frac{3}{48}$ to lowest terms by extracting and canceling out $3$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{1}{16}\left(3-15x\right)\times 3x_{5}-\frac{1}{2}$$

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

$$\frac{35}{9}-\frac{10}{3}x-\frac{3}{16}\left(3-15x\right)x_{5}-\frac{1}{2}$$

Use the distributive property to multiply $-\frac{3}{16}$ by $3-15x$.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{3}{16}\times 3-\frac{3}{16}\left(-15\right)x\right)x_{5}-\frac{1}{2}$$

Express $-\frac{3}{16}\times 3$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x+\left(\frac{-3\times 3}{16}-\frac{3}{16}\left(-15\right)x\right)x_{5}-\frac{1}{2}$$

Multiply $-3$ and $3$ to get $-9$.

$$\frac{35}{9}-\frac{10}{3}x+\left(\frac{-9}{16}-\frac{3}{16}\left(-15\right)x\right)x_{5}-\frac{1}{2}$$

Fraction $\frac{-9}{16}$ can be rewritten as $-\frac{9}{16}$ by extracting the negative sign.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{9}{16}-\frac{3}{16}\left(-15\right)x\right)x_{5}-\frac{1}{2}$$

Express $-\frac{3}{16}\left(-15\right)$ as a single fraction.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{9}{16}+\frac{-3\left(-15\right)}{16}x\right)x_{5}-\frac{1}{2}$$

Multiply $-3$ and $-15$ to get $45$.

$$\frac{35}{9}-\frac{10}{3}x+\left(-\frac{9}{16}+\frac{45}{16}x\right)x_{5}-\frac{1}{2}$$

Use the distributive property to multiply $-\frac{9}{16}+\frac{45}{16}x$ by $x_{5}$.

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{16}x_{5}+\frac{45}{16}xx_{5}-\frac{1}{2}$$

Least common multiple of $9$ and $2$ is $18$. Convert $\frac{35}{9}$ and $\frac{1}{2}$ to fractions with denominator $18$.

$$\frac{70}{18}-\frac{10}{3}x-\frac{9}{16}x_{5}+\frac{45}{16}xx_{5}-\frac{9}{18}$$

Since $\frac{70}{18}$ and $\frac{9}{18}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{70-9}{18}-\frac{10}{3}x-\frac{9}{16}x_{5}+\frac{45}{16}xx_{5}$$

Subtract $9$ from $70$ to get $61$.

$$\frac{61}{18}-\frac{10}{3}x-\frac{9}{16}x_{5}+\frac{45}{16}xx_{5}$$