Question

Solve for x.−4/5x+3/10<8/10

Answer 1

$\tt \: - \frac{4}{5} x + \frac{3}{10} < \frac{8}{10}$

Multiply both sides of the inequality by 10

$\tt \: - 8x + 3 < 8$

Move the constant to the right-hand side and change its sign

$\tt \: - 8x < 8 - 3$

Subtract the numbers

$\tt \: - 8x < 5$

Divide both sides of the inequality by -8 and flip the inequality sign

$\boxed{ \mathfrak{x > - \frac{5}{8} }}$

Answer 2

Answer:

x > -5/8

Step-by-step explanation:

Simplify by combining x and 4/5 and then moving 4 to the left side of x

-x * 4/5 + 3/10 < 8/10

-4x/5 + 3/10 < 8/10

Now we cancel the common factor of 8 and 10.

Factor 2 out of 8

-4x/5 + 3/10 < 2(4)/10

2 from 10

-4x/5 + 3/10 < 4/5

Now move all the terms not containing x to the right side

Lets subtract 3/10 from both sides

-4x/5 < 4/5 - 3/10

Now we multiply by 2/2 to write 4/5 with a common denomi.

-4x/5 < 4/5 * 2/2 - 3/10

Now write with a common denom of 10 and multiply by 1

-4x/5 < 4*2/5 * 2 - 3/10

5 by 2

-4x/5 < 4 * 2/10 - 3/10

Combine

-4x/5 < 4 * 2 - 3/10

Simplify the numerator by multiplying then subtracting

-4x/5 < 8 - 3/10

-4x/5 < 5/10

Cancel the common factor of 5 and 10...

-4x/5 < 5(1)/10

-4x/5 5* 1/5 * 2

-4x/5 < 1/2

Now we divide by -1

-4x/5)/-1 > 1/2)/-1

4x/5 > 1/2)-1

4x/5 > -1/2

Multiply both sides by 5 and cancel common factors. (5)

4x * 5 > -1/2 * 5

4x > -1/2 * 5

4x > -5/2

Now divide by 4 in each term

4x/4 > -5/2)/4

x > -5/2)/4

Multiply the numer by the reciprocal of the denom

x > -5/1 * 1/4

x > -5/4 * 2

x > -5/8