Solve the System of Inequalities 4x+3<7 or 3x-8>7

$4 x + 3 < 7$ or $3 x - 8 > 7$

Simplify the first inequality.

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

Subtract $3$ from both sides of the inequality.

$4 x < 7 - 3$ or $3 x - 8 > 7$

Subtract $3$ from $7$ .

$4 x < 4$ or $3 x - 8 > 7$

Divide each term in $4 x < 4$ by $4$ and simplify.

Divide each term in $4 x < 4$ by $4$ .

$\frac{4 x}{4} < \frac{4}{4}$ or $3 x - 8 > 7$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} < \frac{4}{4}$ or $3 x - 8 > 7$

Divide $x$ by $1$ .

$x < \frac{4}{4}$ or $3 x - 8 > 7$

Simplify the right side.

Divide $4$ by $4$ .

$x < 1$ or $3 x - 8 > 7$

Simplify the second inequality.

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

Add $8$ to both sides of the inequality.

$x < 1$ or $3 x > 7 + 8$

Add $7$ and $8$ .

$x < 1$ or $3 x > 15$

Divide each term in $3 x > 15$ by $3$ and simplify.

Divide each term in $3 x > 15$ by $3$ .

$x < 1$ or $\frac{3 x}{3} > \frac{15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$x < 1$ or $\frac{3 x}{3} > \frac{15}{3}$

Divide $x$ by $1$ .

$x < 1$ or $x > \frac{15}{3}$

Simplify the right side.

Divide $15$ by $3$ .

$x < 1$ or $x > 5$

The result can be shown in multiple forms.

Inequality Form:

$x < 1 or x > 5$

Interval Notation:

$(- \infty, 1) \cup (5, \infty)$