Solve \frac { 2 } { 3 } ( x - 5 ) - \frac { 1 } { 4 } ( x - 2 ) = \frac { 9 } { 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

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

Solve for x

$x = \frac{88}{5} = 17\frac{3}{5} = 17.6$

Steps for Solving Linear Equation

Use the distributive property to multiply $\frac{2}{3}$ by $x-5$.

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

Express $\frac{2}{3}\left(-5\right)$ as a single fraction.

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

Multiply $2$ and $-5$ to get $-10$.

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

Fraction $\frac{-10}{3}$ can be rewritten as $-\frac{10}{3}$ by extracting the negative sign.

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

Use the distributive property to multiply $-\frac{1}{4}$ by $x-2$.

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

Express $-\frac{1}{4}\left(-2\right)$ as a single fraction.

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

Multiply $-1$ and $-2$ to get $2$.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{2}{4}=\frac{9}{2}$$

Reduce the fraction $\frac{2}{4}$ to lowest terms by extracting and canceling out $2$.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{1}{2}=\frac{9}{2}$$

Combine $\frac{2}{3}x$ and $-\frac{1}{4}x$ to get $\frac{5}{12}x$.

$$\frac{5}{12}x-\frac{10}{3}+\frac{1}{2}=\frac{9}{2}$$

Least common multiple of $3$ and $2$ is $6$. Convert $-\frac{10}{3}$ and $\frac{1}{2}$ to fractions with denominator $6$.

$$\frac{5}{12}x-\frac{20}{6}+\frac{3}{6}=\frac{9}{2}$$

Since $-\frac{20}{6}$ and $\frac{3}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{5}{12}x+\frac{-20+3}{6}=\frac{9}{2}$$

Add $-20$ and $3$ to get $-17$.

$$\frac{5}{12}x-\frac{17}{6}=\frac{9}{2}$$

Add $\frac{17}{6}$ to both sides.

$$\frac{5}{12}x=\frac{9}{2}+\frac{17}{6}$$

Least common multiple of $2$ and $6$ is $6$. Convert $\frac{9}{2}$ and $\frac{17}{6}$ to fractions with denominator $6$.

$$\frac{5}{12}x=\frac{27}{6}+\frac{17}{6}$$

Since $\frac{27}{6}$ and $\frac{17}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{5}{12}x=\frac{27+17}{6}$$

Add $27$ and $17$ to get $44$.

$$\frac{5}{12}x=\frac{44}{6}$$

Reduce the fraction $\frac{44}{6}$ to lowest terms by extracting and canceling out $2$.

$$\frac{5}{12}x=\frac{22}{3}$$

Multiply both sides by $\frac{12}{5}$, the reciprocal of $\frac{5}{12}$.

$$x=\frac{22}{3}\times \frac{12}{5}$$

Multiply $\frac{22}{3}$ times $\frac{12}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{22\times 12}{3\times 5}$$

Do the multiplications in the fraction $\frac{22\times 12}{3\times 5}$.

$$x=\frac{264}{15}$$

Reduce the fraction $\frac{264}{15}$ to lowest terms by extracting and canceling out $3$.

$$x=\frac{88}{5}$$