Solve (- 7/4 - 2)/3 + 1 = (- 7/4)/7 | 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

$$\frac{-\frac{7}{4}-2}{3}+1=\frac{-\frac{7}{4}}{7}$$

Verify

$\text{true}$

Solution Steps

Multiply both sides of the equation by $21$, the least common multiple of $3,7$.

$$7\left(-\frac{7}{4}-2\right)+21=3\left(-\frac{7}{4}\right)$$

Convert $2$ to fraction $\frac{8}{4}$.

$$7\left(-\frac{7}{4}-\frac{8}{4}\right)+21=3\left(-\frac{7}{4}\right)$$

Since $-\frac{7}{4}$ and $\frac{8}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$7\times \frac{-7-8}{4}+21=3\left(-\frac{7}{4}\right)$$

Subtract $8$ from $-7$ to get $-15$.

$$7\left(-\frac{15}{4}\right)+21=3\left(-\frac{7}{4}\right)$$

Express $7\left(-\frac{15}{4}\right)$ as a single fraction.

$$\frac{7\left(-15\right)}{4}+21=3\left(-\frac{7}{4}\right)$$

Multiply $7$ and $-15$ to get $-105$.

$$\frac{-105}{4}+21=3\left(-\frac{7}{4}\right)$$

Fraction $\frac{-105}{4}$ can be rewritten as $-\frac{105}{4}$ by extracting the negative sign.

$$-\frac{105}{4}+21=3\left(-\frac{7}{4}\right)$$

Convert $21$ to fraction $\frac{84}{4}$.

$$-\frac{105}{4}+\frac{84}{4}=3\left(-\frac{7}{4}\right)$$

Since $-\frac{105}{4}$ and $\frac{84}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{-105+84}{4}=3\left(-\frac{7}{4}\right)$$

Add $-105$ and $84$ to get $-21$.

$$-\frac{21}{4}=3\left(-\frac{7}{4}\right)$$

Express $3\left(-\frac{7}{4}\right)$ as a single fraction.

$$-\frac{21}{4}=\frac{3\left(-7\right)}{4}$$

Multiply $3$ and $-7$ to get $-21$.

$$-\frac{21}{4}=\frac{-21}{4}$$

Fraction $\frac{-21}{4}$ can be rewritten as $-\frac{21}{4}$ by extracting the negative sign.

$$-\frac{21}{4}=-\frac{21}{4}$$

Compare $-\frac{21}{4}$ and $-\frac{21}{4}$.

$$\text{true}$$