Solve 9x * (- 13/5) + 5 = 4(- 13/5 - 2) | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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

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Question

$$9x\frac{-13}{5}+5=4(\frac{-13}{5}-2)$$

Solve for x

$x=1$

Steps for Solving Linear Equation

Fraction $\frac{-13}{5}$ can be rewritten as $-\frac{13}{5}$ by extracting the negative sign.

$$9x\left(-\frac{13}{5}\right)+5=4\left(\frac{-13}{5}-2\right)$$

Express $9\left(-\frac{13}{5}\right)$ as a single fraction.

$$\frac{9\left(-13\right)}{5}x+5=4\left(\frac{-13}{5}-2\right)$$

Multiply $9$ and $-13$ to get $-117$.

$$\frac{-117}{5}x+5=4\left(\frac{-13}{5}-2\right)$$

Fraction $\frac{-117}{5}$ can be rewritten as $-\frac{117}{5}$ by extracting the negative sign.

$$-\frac{117}{5}x+5=4\left(\frac{-13}{5}-2\right)$$

Fraction $\frac{-13}{5}$ can be rewritten as $-\frac{13}{5}$ by extracting the negative sign.

$$-\frac{117}{5}x+5=4\left(-\frac{13}{5}-2\right)$$

Convert $2$ to fraction $\frac{10}{5}$.

$$-\frac{117}{5}x+5=4\left(-\frac{13}{5}-\frac{10}{5}\right)$$

Since $-\frac{13}{5}$ and $\frac{10}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{117}{5}x+5=4\times \frac{-13-10}{5}$$

Subtract $10$ from $-13$ to get $-23$.

$$-\frac{117}{5}x+5=4\left(-\frac{23}{5}\right)$$

Express $4\left(-\frac{23}{5}\right)$ as a single fraction.

$$-\frac{117}{5}x+5=\frac{4\left(-23\right)}{5}$$

Multiply $4$ and $-23$ to get $-92$.

$$-\frac{117}{5}x+5=\frac{-92}{5}$$

Fraction $\frac{-92}{5}$ can be rewritten as $-\frac{92}{5}$ by extracting the negative sign.

$$-\frac{117}{5}x+5=-\frac{92}{5}$$

Subtract $5$ from both sides.

$$-\frac{117}{5}x=-\frac{92}{5}-5$$

Convert $5$ to fraction $\frac{25}{5}$.

$$-\frac{117}{5}x=-\frac{92}{5}-\frac{25}{5}$$

Since $-\frac{92}{5}$ and $\frac{25}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{117}{5}x=\frac{-92-25}{5}$$

Subtract $25$ from $-92$ to get $-117$.

$$-\frac{117}{5}x=-\frac{117}{5}$$

Multiply both sides by $-\frac{5}{117}$, the reciprocal of $-\frac{117}{5}$.

$$x=-\frac{117}{5}\left(-\frac{5}{117}\right)$$

Multiply $-\frac{117}{5}$ times $-\frac{5}{117}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-117\left(-5\right)}{5\times 117}$$

Do the multiplications in the fraction $\frac{-117\left(-5\right)}{5\times 117}$.

$$x=\frac{585}{585}$$

Divide $585$ by $585$ to get $1$.

$$x=1$$