Solve the Inequality for x 5(5-4x)+7x<4(7+4x)

$5 (5 - 4 x) + 7 x < 4 (7 + 4 x)$

Step 1

Simplify $5 (5 - 4 x) + 7 x$ .

Simplify each term.

Apply the distributive property.

$5 \cdot 5 + 5 (- 4 x) + 7 x < 4 (7 + 4 x)$

Multiply $5$ by $5$ .

$25 + 5 (- 4 x) + 7 x < 4 (7 + 4 x)$

Multiply $- 4$ by $5$ .

$25 - 20 x + 7 x < 4 (7 + 4 x)$

Add $- 20 x$ and $7 x$ .

$25 - 13 x < 4 (7 + 4 x)$

Step 2

Simplify $4 (7 + 4 x)$ .

Apply the distributive property.

$25 - 13 x < 4 \cdot 7 + 4 (4 x)$

Multiply.

Multiply $4$ by $7$ .

$25 - 13 x < 28 + 4 (4 x)$

Multiply $4$ by $4$ .

$25 - 13 x < 28 + 16 x$

Step 3

Move all terms containing $x$ to the left side of the inequality.

Subtract $16 x$ from both sides of the inequality.

$25 - 13 x - 16 x < 28$

Subtract $16 x$ from $- 13 x$ .

$25 - 29 x < 28$

Step 4

Move all terms not containing $x$ to the right side of the inequality.

Subtract $25$ from both sides of the inequality.

$- 29 x < 28 - 25$

Subtract $25$ from $28$ .

$- 29 x < 3$

Step 5

Divide each term in $- 29 x < 3$ by $- 29$ and simplify.

Divide each term in $- 29 x < 3$ by $- 29$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 29 x}{- 29} > \frac{3}{- 29}$

Simplify the left side.

Cancel the common factor of $- 29$ .

Cancel the common factor.

$\frac{- 29 x}{- 29} > \frac{3}{- 29}$

Divide $x$ by $1$ .

$x > \frac{3}{- 29}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{3}{29}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{3}{29}$

Interval Notation:

$(- \frac{3}{29}, \infty)$

Solve the Inequality for x 5(5-4x)+7x<4(7+4x)

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