Solve (x)/(2)+(13)/(10) <= (x)/(5)+1 | 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

$$\frac{ x }{ 2 } + \frac{ 13 }{ 10 } \leq \frac{ x }{ 5 } +1$$

Solve for x

$x\leq -1$

Solution Steps

Multiply both sides of the equation by $10$, the least common multiple of $2,10,5$. Since $10$ is positive, the inequality direction remains the same.

$$5x+13\leq 2x+10$$

Subtract $2x$ from both sides.

$$5x+13-2x\leq 10$$

Combine $5x$ and $-2x$ to get $3x$.

$$3x+13\leq 10$$

Subtract $13$ from both sides.

$$3x\leq 10-13$$

Subtract $13$ from $10$ to get $-3$.

$$3x\leq -3$$

Divide both sides by $3$. Since $3$ is positive, the inequality direction remains the same.

$$x\leq \frac{-3}{3}$$

Divide $-3$ by $3$ to get $-1$.

$$x\leq -1$$