Solve x/2 < (5x-2)/3-(7x-3)/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

$$x/2 < (5x-2)/3-(7x-3)/5$$

Solve for x

$x<-\frac{2}{7}$

Solution Steps

Multiply both sides of the equation by $30$, the least common multiple of $2,3,5$. Since $30$ is positive, the inequality direction remains the same.

$$15x<10\left(5x-2\right)-6\left(7x-3\right)$$

Use the distributive property to multiply $10$ by $5x-2$.

$$15x<50x-20-6\left(7x-3\right)$$

Use the distributive property to multiply $-6$ by $7x-3$.

$$15x<50x-20-42x+18$$

Combine $50x$ and $-42x$ to get $8x$.

$$15x<8x-20+18$$

Add $-20$ and $18$ to get $-2$.

$$15x<8x-2$$

Subtract $8x$ from both sides.

$$15x-8x<-2$$

Combine $15x$ and $-8x$ to get $7x$.

$$7x<-2$$

Divide both sides by $7$. Since $7$ is positive, the inequality direction remains the same.

$$x<-\frac{2}{7}$$