Algebra Examples

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

Step 1

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

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Step 1.1

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

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

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

Step 1.1.1.2

Multiply $5$ by $5$ .

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

Step 1.1.1.3

Multiply $- 4$ by $5$ .

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

Step 1.1.2

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

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

Step 1.2

Simplify $4 (7 + 4 x)$ .

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Multiply.

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Step 1.2.2.1

Multiply $4$ by $7$ .

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

Step 1.2.2.2

Multiply $4$ by $4$ .

$25 - 13 x < 28 + 16 x$

Step 1.3

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

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Step 1.3.1

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

$25 - 13 x - 16 x < 28$

Step 1.3.2

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

$25 - 29 x < 28$

Step 1.4

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

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Step 1.4.1

Subtract $25$ from both sides of the inequality.

$- 29 x < 28 - 25$

Step 1.4.2

Subtract $25$ from $28$ .

$- 29 x < 3$

Step 1.5

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

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Step 1.5.1

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.

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

Step 1.5.2

Simplify the left side.

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Step 1.5.2.1

Cancel the common factor of $- 29$ .

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Step 1.5.2.1.1

Cancel the common factor.

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

Step 1.5.2.1.2

Divide $x$ by $1$ .

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

Step 1.5.3

Simplify the right side.

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Step 1.5.3.1

Move the negative in front of the fraction.

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

Step 2

Use the inequality $x > - \frac{3}{29}$ to build the set notation.

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

Step 3