Algebra Examples

$3 m + 2 < 5$ OR $\frac{m + 1}{2} > 4$

Step 1

Solve $3 m + 2 < 5$ for $m$ .

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Step 1.1

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

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Step 1.1.1

Subtract $2$ from both sides of the inequality.

$3 m < 5 - 2$

Step 1.1.2

Subtract $2$ from $5$ .

$3 m < 3$

Step 1.2

Divide each term in $3 m < 3$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 m < 3$ by $3$ .

$\frac{3 m}{3} < \frac{3}{3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 m}{3} < \frac{3}{3}$

Step 1.2.2.1.2

Divide $m$ by $1$ .

$m < \frac{3}{3}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $3$ by $3$ .

$m < 1$

Step 2

Solve $\frac{m + 1}{2} > 4$ for $m$ .

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Step 2.1

Multiply both sides by $2$ .

$\frac{m + 1}{2} \cdot 2 > 4 \cdot 2$

Step 2.2

Simplify.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{m + 1}{2} \cdot 2 > 4 \cdot 2$

Step 2.2.1.1.2

Rewrite the expression.

$m + 1 > 4 \cdot 2$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Multiply $4$ by $2$ .

$m + 1 > 8$

Step 2.3

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

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Step 2.3.1

Subtract $1$ from both sides of the inequality.

$m > 8 - 1$

Step 2.3.2

Subtract $1$ from $8$ .

$m > 7$

Step 3

Find the intersection of $m < 1$ and $m > 7$ .

No solution