Answer: The simpler equivalent form 4x + 9 =7.
Final answer [tex]x = -\frac{1}{2}[/tex].
Step-by-step explanation: Given equation
[tex]\frac{2x}{5} +\frac{9}{10} =\frac{7}{10}[/tex].
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,
[tex]10\times\frac{2x}{5} +10\times\frac{9}{10} =10\times\frac{7}{10}[/tex]
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
[tex]\frac{4x}{4} =\frac{-2}{4}[/tex]
[tex]x = -\frac{1}{2}[/tex]
