Algebra Examples

$14 r + 20 < 14 r + 16$ or $8 - 10 r \geq 15 - 9 r$

Step 1

Simplify the first inequality.

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Step 1.1

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

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Step 1.1.1

Subtract $14 r$ from both sides of the inequality.

$14 r + 20 - 14 r < 16$ or $8 - 10 r \geq 15 - 9 r$

Step 1.1.2

Combine the opposite terms in $14 r + 20 - 14 r$ .

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Step 1.1.2.1

Subtract $14 r$ from $14 r$ .

$0 + 20 < 16$ or $8 - 10 r \geq 15 - 9 r$

Step 1.1.2.2

Add $0$ and $20$ .

$20 < 16$ or $8 - 10 r \geq 15 - 9 r$

Step 1.2

Since $20 > 16$ , there are no solutions.

No solution or $8 - 10 r \geq 15 - 9 r$

No solution

Step 2

Simplify the second inequality.

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Step 2.1

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

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Step 2.1.1

Add $9 r$ to both sides of the inequality.

No solution or $8 - 10 r + 9 r \geq 15$

Step 2.1.2

Add $- 10 r$ and $9 r$ .

No solution or $8 - r \geq 15$

Step 2.2

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

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Step 2.2.1

Subtract $8$ from both sides of the inequality.

No solution or $- r \geq 15 - 8$

Step 2.2.2

Subtract $8$ from $15$ .

No solution or $- r \geq 7$

Step 2.3

Divide each term in $- r \geq 7$ by $- 1$ and simplify.

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Step 2.3.1

Divide each term in $- r \geq 7$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

No solution or $\frac{- r}{- 1} \leq \frac{7}{- 1}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Dividing two negative values results in a positive value.

No solution or $\frac{r}{1} \leq \frac{7}{- 1}$

Step 2.3.2.2

Divide $r$ by $1$ .

No solution or $r \leq \frac{7}{- 1}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $7$ by $- 1$ .

No solution or $r \leq - 7$

No solution