Solve the System of Inequalities 3x-1<=8 and 3x-1<35

$3 x - 1 \leq 8$ and $3 x - 1 < 35$

Step 1

Simplify the first inequality.

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

Add $1$ to both sides of the inequality.

$3 x \leq 8 + 1$ and $3 x - 1 < 35$

Add $8$ and $1$ .

$3 x \leq 9$ and $3 x - 1 < 35$

Divide each term in $3 x \leq 9$ by $3$ and simplify.

Divide each term in $3 x \leq 9$ by $3$ .

$\frac{3 x}{3} \leq \frac{9}{3}$ and $3 x - 1 < 35$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{9}{3}$ and $3 x - 1 < 35$

Divide $x$ by $1$ .

$x \leq \frac{9}{3}$ and $3 x - 1 < 35$

Simplify the right side.

Divide $9$ by $3$ .

$x \leq 3$ and $3 x - 1 < 35$

Step 2

Simplify the second inequality.

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

Add $1$ to both sides of the inequality.

$x \leq 3$ and $3 x < 35 + 1$

Add $35$ and $1$ .

$x \leq 3$ and $3 x < 36$

Divide each term in $3 x < 36$ by $3$ and simplify.

Divide each term in $3 x < 36$ by $3$ .

$x \leq 3$ and $\frac{3 x}{3} < \frac{36}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$x \leq 3$ and $\frac{3 x}{3} < \frac{36}{3}$

Divide $x$ by $1$ .

$x \leq 3$ and $x < \frac{36}{3}$

Simplify the right side.

Divide $36$ by $3$ .

$x \leq 3$ and $x < 12$

Step 3

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

$x \leq 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 3$

Interval Notation:

$(- \infty, 3]$

Step 5

Solve the System of Inequalities 3x-1<=8 and 3x-1<35

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