Pre-Algebra Examples

$3 (4 x + 1) \leq 39$

Step 1

Divide each term in $3 (4 x + 1) \leq 39$ by $3$ and simplify.

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Step 1.1

Divide each term in $3 (4 x + 1) \leq 39$ by $3$ .

$\frac{3 (4 x + 1)}{3} \leq \frac{39}{3}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $3$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{3 (4 x + 1)}{3} \leq \frac{39}{3}$

Step 1.2.1.2

Divide $4 x + 1$ by $1$ .

$4 x + 1 \leq \frac{39}{3}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $39$ by $3$ .

$4 x + 1 \leq 13$

Step 2

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

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Step 2.1

Subtract $1$ from both sides of the inequality.

$4 x \leq 13 - 1$

Step 2.2

Subtract $1$ from $13$ .

$4 x \leq 12$

Step 3

Divide each term in $4 x \leq 12$ by $4$ and simplify.

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Step 3.1

Divide each term in $4 x \leq 12$ by $4$ .

$\frac{4 x}{4} \leq \frac{12}{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} \leq \frac{12}{4}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{12}{4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $12$ by $4$ .

$x \leq 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 3$

Interval Notation:

$(- \infty, 3]$