Question

solve the equation. check each solution to verify the solution is valid.

1. $\frac{2x}{5} + \frac{1}{2} = \frac{3x}{10}$

answer: _______________

Explanation:

Step1: Eliminate denominators via LCD

Multiply all terms by 10 (LCD of 5,2,10):
$$10\times\frac{2x}{5} + 10\times\frac{1}{2} = 10\times\frac{3x}{10}$$

Step2: Simplify each term

Calculate each product:
$$4x + 5 = 3x$$

Step3: Isolate x on one side

Subtract $3x$ from both sides:
$$4x - 3x + 5 = 0$$

Step4: Solve for x

Simplify and rearrange:
$$x = -5$$

Step5: Verify the solution

Substitute $x=-5$ into original equation:
$$\frac{2(-5)}{5} + \frac{1}{2} = \frac{3(-5)}{10}$$
$$-2 + \frac{1}{2} = -\frac{15}{10}$$
$$-\frac{3}{2} = -\frac{3}{2}$$
The solution is valid.

Answer:

$x=-5$