Solve the System of Inequalities 7x+39>=53 AND 16x+15>31

$7 x + 39 \geq 53$ AND $16 x + 15 > 31$

Step 1

Solve $7 x + 39 \geq 53$ for $x$ .

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

Subtract $39$ from both sides of the inequality.

$7 x \geq 53 - 39$

Subtract $39$ from $53$ .

$7 x \geq 14$

Divide each term in $7 x \geq 14$ by $7$ and simplify.

Divide each term in $7 x \geq 14$ by $7$ .

$\frac{7 x}{7} \geq \frac{14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} \geq \frac{14}{7}$

Divide $x$ by $1$ .

$x \geq \frac{14}{7}$

Simplify the right side.

Divide $14$ by $7$ .

$x \geq 2$

Step 2

Solve $16 x + 15 > 31$ for $x$ .

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

Subtract $15$ from both sides of the inequality.

$16 x > 31 - 15$

Subtract $15$ from $31$ .

$16 x > 16$

Divide each term in $16 x > 16$ by $16$ and simplify.

Divide each term in $16 x > 16$ by $16$ .

$\frac{16 x}{16} > \frac{16}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} > \frac{16}{16}$

Divide $x$ by $1$ .

$x > \frac{16}{16}$

Simplify the right side.

Divide $16$ by $16$ .

$x > 1$

Step 3

Find the intersection of $x \geq 2$ and $x > 1$ .

$x \geq 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 2$

Interval Notation:

$[2, \infty)$

Step 5

Solve the System of Inequalities 7x+39>=53 AND 16x+15>31

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