Algebra Examples

$- 5 x - 3 \geq 2$ and $4 x - 2 \geq 5$

Step 1

Simplify the first inequality.

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Step 1.1

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

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Step 1.1.1

Add $3$ to both sides of the inequality.

$- 5 x \geq 2 + 3$

Step 1.1.2

Add $2$ and $3$ .

$- 5 x \geq 5$

Step 1.2

Divide each term in $- 5 x \geq 5$ by $- 5$ and simplify.

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Step 1.2.1

Divide each term in $- 5 x \geq 5$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \leq \frac{5}{- 5}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} \leq \frac{5}{- 5}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{5}{- 5}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $5$ by $- 5$ .

$x \leq - 1$

Step 2

Simplify the second inequality.

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Step 2.1

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

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Step 2.1.1

Add $2$ to both sides of the inequality.

$4 x \geq 5 + 2$

Step 2.1.2

Add $5$ and $2$ .

$4 x \geq 7$

Step 2.2

Divide each term in $4 x \geq 7$ by $4$ and simplify.

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Step 2.2.1

Divide each term in $4 x \geq 7$ by $4$ .

$\frac{4 x}{4} \geq \frac{7}{4}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{7}{4}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{7}{4}$

Step 3

The intersection consists of the elements that are contained in both intervals.

No solution