Algebra Examples

$\frac{7 x + 6}{2} \leq 3 x + 2$

Step 1

Multiply both sides by $2$ .

$\frac{7 x + 6}{2} \cdot 2 \leq (3 x + 2) \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{7 x + 6}{2} \cdot 2 \leq (3 x + 2) \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$7 x + 6 \leq (3 x + 2) \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(3 x + 2) \cdot 2$ .

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Step 2.2.1.1

Apply the distributive property.

$7 x + 6 \leq 3 x \cdot 2 + 2 \cdot 2$

Step 2.2.1.2

Multiply.

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Step 2.2.1.2.1

Multiply $2$ by $3$ .

$7 x + 6 \leq 6 x + 2 \cdot 2$

Step 2.2.1.2.2

Multiply $2$ by $2$ .

$7 x + 6 \leq 6 x + 4$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $6 x$ from both sides of the inequality.

$7 x + 6 - 6 x \leq 4$

Step 3.1.2

Subtract $6 x$ from $7 x$ .

$x + 6 \leq 4$

Step 3.2

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

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Step 3.2.1

Subtract $6$ from both sides of the inequality.

$x \leq 4 - 6$

Step 3.2.2

Subtract $6$ from $4$ .

$x \leq - 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 2$

Interval Notation:

$(- \infty, - 2]$