Question

Rewrite the equation to a simpler equivalent form, then solve for x.

Answer 1

Answer: The simpler equivalent form 4x + 9 =7.

Final answer $x = -\frac{1}{2}$.

Step-by-step explanation: Given equation

$\frac{2x}{5} +\frac{9}{10} =\frac{7}{10}$.

First we need to write it in simpler form and then solve for x.

In order to write it in simpler equivalent form, we need to find the common denominator/ least common denominator.

We have 5, 10 and 10 in denominators.

LCM of 5 and 10 is 10.

Therefore, we need to multiply each term by 10 on the top  and simplify to remove denominators.

Therefore,

$10\times\frac{2x}{5} +10\times\frac{9}{10} =10\times\frac{7}{10}$

On simplifying this step, we get

2 × 2x + 9 = 7

4x + 9 =7.

This the simpler equivalent form.

Now, subtracting 9 from both sides, we get

4x+9-9 = 7-9

4x = -2

Dividing both sides by 4, we get

$\frac{4x}{4} =\frac{-2}{4}$

$x = -\frac{1}{2}$