Solve 5/9 * (7 - 6x) - 3/4 * (3 - 15x) = 1/2 * (3x - 5) * 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

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

Solve for x

$x=-\frac{52}{129}\approx -0.403100775$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

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

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

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

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

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

Use the distributive property to multiply $-\frac{3}{4}$ by $3-15x$.

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

Express $-\frac{3}{4}\times 3$ as a single fraction.

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

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

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

Fraction $\frac{-9}{4}$ can be rewritten as $-\frac{9}{4}$ by extracting the negative sign.

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

Express $-\frac{3}{4}\left(-15\right)$ as a single fraction.

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

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

$$\frac{35}{9}-\frac{10}{3}x-\frac{9}{4}+\frac{45}{4}x=\frac{1}{2}\left(3x-5\right)\times \frac{1}{2}$$

Least common multiple of $9$ and $4$ is $36$. Convert $\frac{35}{9}$ and $\frac{9}{4}$ to fractions with denominator $36$.

$$\frac{140}{36}-\frac{10}{3}x-\frac{81}{36}+\frac{45}{4}x=\frac{1}{2}\left(3x-5\right)\times \frac{1}{2}$$

Since $\frac{140}{36}$ and $\frac{81}{36}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{140-81}{36}-\frac{10}{3}x+\frac{45}{4}x=\frac{1}{2}\left(3x-5\right)\times \frac{1}{2}$$

Subtract $81$ from $140$ to get $59$.

$$\frac{59}{36}-\frac{10}{3}x+\frac{45}{4}x=\frac{1}{2}\left(3x-5\right)\times \frac{1}{2}$$

Combine $-\frac{10}{3}x$ and $\frac{45}{4}x$ to get $\frac{95}{12}x$.

$$\frac{59}{36}+\frac{95}{12}x=\frac{1}{2}\left(3x-5\right)\times \frac{1}{2}$$

Multiply $\frac{1}{2}$ times $\frac{1}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{59}{36}+\frac{95}{12}x=\frac{1\times 1}{2\times 2}\left(3x-5\right)$$

Do the multiplications in the fraction $\frac{1\times 1}{2\times 2}$.

$$\frac{59}{36}+\frac{95}{12}x=\frac{1}{4}\left(3x-5\right)$$

Use the distributive property to multiply $\frac{1}{4}$ by $3x-5$.

$$\frac{59}{36}+\frac{95}{12}x=\frac{1}{4}\times 3x+\frac{1}{4}\left(-5\right)$$

Multiply $\frac{1}{4}$ and $3$ to get $\frac{3}{4}$.

$$\frac{59}{36}+\frac{95}{12}x=\frac{3}{4}x+\frac{1}{4}\left(-5\right)$$

Multiply $\frac{1}{4}$ and $-5$ to get $\frac{-5}{4}$.

$$\frac{59}{36}+\frac{95}{12}x=\frac{3}{4}x+\frac{-5}{4}$$

Fraction $\frac{-5}{4}$ can be rewritten as $-\frac{5}{4}$ by extracting the negative sign.

$$\frac{59}{36}+\frac{95}{12}x=\frac{3}{4}x-\frac{5}{4}$$

Subtract $\frac{3}{4}x$ from both sides.

$$\frac{59}{36}+\frac{95}{12}x-\frac{3}{4}x=-\frac{5}{4}$$

Combine $\frac{95}{12}x$ and $-\frac{3}{4}x$ to get $\frac{43}{6}x$.

$$\frac{59}{36}+\frac{43}{6}x=-\frac{5}{4}$$

Subtract $\frac{59}{36}$ from both sides.

$$\frac{43}{6}x=-\frac{5}{4}-\frac{59}{36}$$

Least common multiple of $4$ and $36$ is $36$. Convert $-\frac{5}{4}$ and $\frac{59}{36}$ to fractions with denominator $36$.

$$\frac{43}{6}x=-\frac{45}{36}-\frac{59}{36}$$

Since $-\frac{45}{36}$ and $\frac{59}{36}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{43}{6}x=\frac{-45-59}{36}$$

Subtract $59$ from $-45$ to get $-104$.

$$\frac{43}{6}x=\frac{-104}{36}$$

Reduce the fraction $\frac{-104}{36}$ to lowest terms by extracting and canceling out $4$.

$$\frac{43}{6}x=-\frac{26}{9}$$

Multiply both sides by $\frac{6}{43}$, the reciprocal of $\frac{43}{6}$.

$$x=-\frac{26}{9}\times \frac{6}{43}$$

Multiply $-\frac{26}{9}$ times $\frac{6}{43}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-26\times 6}{9\times 43}$$

Do the multiplications in the fraction $\frac{-26\times 6}{9\times 43}$.

$$x=\frac{-156}{387}$$

Reduce the fraction $\frac{-156}{387}$ to lowest terms by extracting and canceling out $3$.

$$x=-\frac{52}{129}$$