Solve 3-5(-7g-4)>9g-85g

Question

Solve the inequality

g > - \frac{23}{111}

Alternative Form

g \in (- \frac{23}{111}, + \infty)

Evaluate

3 - 5 (- 7 g - 4) > 9 g - 85 g

Subtract the terms

More Steps

Evaluate

9 g - 85 g

Collect like terms by calculating the sum or difference of their coefficients

(9 - 85) g

Subtract the numbers

- 76 g

3 - 5 (- 7 g - 4) > - 76 g

Move the expression to the left side

3 - 5 (- 7 g - 4) - (- 76 g) > 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

3 - 5 (- 7 g - 4) + 76 g > 0

Calculate the sum or difference

More Steps

Evaluate

3 - 5 (- 7 g - 4) + 76 g

Expand the expression

More Steps

Calculate

- 5 (- 7 g - 4)

Apply the distributive property

- 5 (- 7 g) - (- 5 \times 4)

Multiply the numbers

35 g - (- 5 \times 4)

Multiply the numbers

35 g - (- 20)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

35 g + 20

3 + 35 g + 20 + 76 g

Add the numbers

23 + 35 g + 76 g

Add the terms

More Steps

Evaluate

35 g + 76 g

Collect like terms by calculating the sum or difference of their coefficients

(35 + 76) g

Add the numbers

111 g

23 + 111 g

23 + 111 g > 0

Move the constant to the right side

111 g > 0 - 23

Removing 0 doesn't change the value,so remove it from the expression

111 g > - 23

Divide both sides

\frac{111 g}{111} > \frac{- 23}{111}

Divide the numbers

g > \frac{- 23}{111}

Solution

g > - \frac{23}{111}

Alternative Form

g \in (- \frac{23}{111}, + \infty)

Show Solution