Solve (4x+5)/(15)=(7x+2)/(3)+(5x+2)/(5) | 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

$$\frac{ 4x+5 }{ 15 } = \frac{ 7x+2 }{ 3 } + \frac{ 5x+2 }{ 5 }$$

Solve for x

$x=-\frac{11}{46}\approx -0.239130435$

Steps for Solving Linear Equation

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

$$4x+5=5\left(7x+2\right)+3\left(5x+2\right)$$

Use the distributive property to multiply $5$ by $7x+2$.

$$4x+5=35x+10+3\left(5x+2\right)$$

Use the distributive property to multiply $3$ by $5x+2$.

$$4x+5=35x+10+15x+6$$

Combine $35x$ and $15x$ to get $50x$.

$$4x+5=50x+10+6$$

Add $10$ and $6$ to get $16$.

$$4x+5=50x+16$$

Subtract $50x$ from both sides.

$$4x+5-50x=16$$

Combine $4x$ and $-50x$ to get $-46x$.

$$-46x+5=16$$

Subtract $5$ from both sides.

$$-46x=16-5$$

Subtract $5$ from $16$ to get $11$.

$$-46x=11$$

Divide both sides by $-46$.

$$x=\frac{11}{-46}$$

Fraction $\frac{11}{-46}$ can be rewritten as $-\frac{11}{46}$ by extracting the negative sign.

$$x=-\frac{11}{46}$$