Solve (12x)/5 - (7x)/3 + 5 = (3x)/10 / 1; 2 * 2 - 3 = 12N | 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

$$\frac{12x}{5}-\frac{7x}{3}+5=\frac{3x}{10}\div1; 2\cdot2-3=12\cdot N$$

Solve for x, N

$x = \frac{150}{7} = 21\frac{3}{7} \approx 21.428571429$
$N=\frac{1}{12}\approx 0.083333333$

Solution Steps

Consider the first equation. Multiply both sides of the equation by $15$, the least common multiple of $5,3$.

$$3\times 12x-5\times 7x+75=15\times \frac{3x}{10}$$

Multiply $3$ and $12$ to get $36$.

$$36x-5\times 7x+75=15\times \frac{3x}{10}$$

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

$$36x-35x+75=15\times \frac{3x}{10}$$

Combine $36x$ and $-35x$ to get $x$.

$$x+75=15\times \frac{3x}{10}$$

Express $15\times \frac{3x}{10}$ as a single fraction.

$$x+75=\frac{15\times 3x}{10}$$

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

$$x+75=\frac{45x}{10}$$

Divide $45x$ by $10$ to get $\frac{9}{2}x$.

$$x+75=\frac{9}{2}x$$

Subtract $\frac{9}{2}x$ from both sides.

$$x+75-\frac{9}{2}x=0$$

Combine $x$ and $-\frac{9}{2}x$ to get $-\frac{7}{2}x$.

$$-\frac{7}{2}x+75=0$$

Subtract $75$ from both sides. Anything subtracted from zero gives its negation.

$$-\frac{7}{2}x=-75$$

Multiply both sides by $-\frac{2}{7}$, the reciprocal of $-\frac{7}{2}$.

$$x=-75\left(-\frac{2}{7}\right)$$

Multiply $-75$ and $-\frac{2}{7}$ to get $\frac{150}{7}$.

$$x=\frac{150}{7}$$

Consider the second equation. Multiply $2$ and $2$ to get $4$.

$$4-3=12N$$

Subtract $3$ from $4$ to get $1$.

$$1=12N$$

Swap sides so that all variable terms are on the left hand side.

$$12N=1$$

Divide both sides by $12$.

$$N=\frac{1}{12}$$

The system is now solved.

$$x=\frac{150}{7}$$ $$N=\frac{1}{12}$$