Pre-Algebra Examples

$\frac{7}{2} x + \frac{1}{2} x = 5 x + \frac{18}{2} + \frac{7}{2} x$

Step 1

Simplify $\frac{7}{2} x + \frac{1}{2} x$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Combine $\frac{7}{2}$ and $x$ .

$\frac{7 x}{2} + \frac{1}{2} x = 5 x + \frac{18}{2} + \frac{7}{2} x$

Step 1.1.2

Combine $\frac{1}{2}$ and $x$ .

$\frac{7 x}{2} + \frac{x}{2} = 5 x + \frac{18}{2} + \frac{7}{2} x$

Step 1.2

Simplify terms.

Tap for more steps...

Step 1.2.1

Combine the numerators over the common denominator.

$\frac{7 x + x}{2} = 5 x + \frac{18}{2} + \frac{7}{2} x$

Step 1.2.2

Add $7 x$ and $x$ .

$\frac{8 x}{2} = 5 x + \frac{18}{2} + \frac{7}{2} x$

Step 1.2.3

Cancel the common factor of $8$ and $2$ .

Tap for more steps...

Step 1.2.3.1

Factor $2$ out of $8 x$ .

$\frac{2 (4 x)}{2} = 5 x + \frac{18}{2} + \frac{7}{2} x$

Step 1.2.3.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.2.1

Factor $2$ out of $2$ .

$\frac{2 (4 x)}{2 (1)} = 5 x + \frac{18}{2} + \frac{7}{2} x$

Step 1.2.3.2.2

Cancel the common factor.

$\frac{2 (4 x)}{2 \cdot 1} = 5 x + \frac{18}{2} + \frac{7}{2} x$

Step 1.2.3.2.3

Rewrite the expression.

$\frac{4 x}{1} = 5 x + \frac{18}{2} + \frac{7}{2} x$

Step 1.2.3.2.4

Divide $4 x$ by $1$ .

$4 x = 5 x + \frac{18}{2} + \frac{7}{2} x$

Step 2

Simplify $5 x + \frac{18}{2} + \frac{7}{2} x$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Divide $18$ by $2$ .

$4 x = 5 x + 9 + \frac{7}{2} x$

Step 2.1.2

Combine $\frac{7}{2}$ and $x$ .

$4 x = 5 x + 9 + \frac{7 x}{2}$

Step 2.2

To write $5 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 x = 5 x \cdot \frac{2}{2} + \frac{7 x}{2} + 9$

Step 2.3

Simplify terms.

Tap for more steps...

Step 2.3.1

Combine $5 x$ and $\frac{2}{2}$ .

$4 x = \frac{5 x \cdot 2}{2} + \frac{7 x}{2} + 9$

Step 2.3.2

Combine the numerators over the common denominator.

$4 x = \frac{5 x \cdot 2 + 7 x}{2} + 9$

Step 2.4

Simplify each term.

Tap for more steps...

Step 2.4.1

Simplify the numerator.

Tap for more steps...

Step 2.4.1.1

Factor $x$ out of $5 x \cdot 2 + 7 x$ .

Tap for more steps...

Step 2.4.1.1.1

Factor $x$ out of $5 x \cdot 2$ .

$4 x = \frac{x (5 \cdot 2) + 7 x}{2} + 9$

Step 2.4.1.1.2

Factor $x$ out of $7 x$ .

$4 x = \frac{x (5 \cdot 2) + x \cdot 7}{2} + 9$

Step 2.4.1.1.3

Factor $x$ out of $x (5 \cdot 2) + x \cdot 7$ .

$4 x = \frac{x (5 \cdot 2 + 7)}{2} + 9$

Step 2.4.1.2

Multiply $5$ by $2$ .

$4 x = \frac{x (10 + 7)}{2} + 9$

Step 2.4.1.3

Add $10$ and $7$ .

$4 x = \frac{x \cdot 17}{2} + 9$

Step 2.4.2

Move $17$ to the left of $x$ .

$4 x = \frac{17 x}{2} + 9$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - 2$

Step 4