Solve the System of @WORD 2x-5<7 , 4x+10>6

$2 x - 5 < 7$ , $4 x + 10 > 6$

Step 1

Solve $2 x - 5 < 7$ for $x$ .

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

Add $5$ to both sides of the inequality.

$2 x < 7 + 5$

Add $7$ and $5$ .

$2 x < 12$

Divide each term in $2 x < 12$ by $2$ and simplify.

Divide each term in $2 x < 12$ by $2$ .

$\frac{2 x}{2} < \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{12}{2}$

Divide $x$ by $1$ .

$x < \frac{12}{2}$

Simplify the right side.

Divide $12$ by $2$ .

$x < 6$

Step 2

Solve $4 x + 10 > 6$ for $x$ .

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

Subtract $10$ from both sides of the inequality.

$4 x > 6 - 10$

Subtract $10$ from $6$ .

$4 x > - 4$

Divide each term in $4 x > - 4$ by $4$ and simplify.

Divide each term in $4 x > - 4$ by $4$ .

$\frac{4 x}{4} > \frac{- 4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{- 4}{4}$

Divide $x$ by $1$ .

$x > \frac{- 4}{4}$

Simplify the right side.

Divide $- 4$ by $4$ .

$x > - 1$

Step 3

Find the intersection of $x < 6$ and $x > - 1$ .

$- 1 < x < 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 1 < x < 6$

Interval Notation:

$(- 1, 6)$

Step 5

Solve the System of @WORD 2x-5<7 , 4x+10>6

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