Algebra Examples

$3 + \frac{3}{2} x + 4 = 4 x - \frac{5}{2} x$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 x - \frac{5}{2} x = 3 + \frac{3}{2} x + 4$

Step 2

Simplify $4 x - \frac{5}{2} x$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

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

$4 x - \frac{x \cdot 5}{2} = 3 + \frac{3}{2} x + 4$

Step 2.1.2

Move $5$ to the left of $x$ .

$4 x - \frac{5 x}{2} = 3 + \frac{3}{2} x + 4$

Step 2.2

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 x \cdot \frac{2}{2} - \frac{5 x}{2} = 3 + \frac{3}{2} x + 4$

Step 2.3

Simplify terms.

Tap for more steps...

Step 2.3.1

Combine $4 x$ and $\frac{2}{2}$ .

$\frac{4 x \cdot 2}{2} - \frac{5 x}{2} = 3 + \frac{3}{2} x + 4$

Step 2.3.2

Combine the numerators over the common denominator.

$\frac{4 x \cdot 2 - 5 x}{2} = 3 + \frac{3}{2} x + 4$

Step 2.4

Simplify the numerator.

Tap for more steps...

Step 2.4.1

Factor $x$ out of $4 x \cdot 2 - 5 x$ .

Tap for more steps...

Step 2.4.1.1

Factor $x$ out of $4 x \cdot 2$ .

$\frac{x (4 \cdot 2) - 5 x}{2} = 3 + \frac{3}{2} x + 4$

Step 2.4.1.2

Factor $x$ out of $- 5 x$ .

$\frac{x (4 \cdot 2) + x \cdot - 5}{2} = 3 + \frac{3}{2} x + 4$

Step 2.4.1.3

Factor $x$ out of $x (4 \cdot 2) + x \cdot - 5$ .

$\frac{x (4 \cdot 2 - 5)}{2} = 3 + \frac{3}{2} x + 4$

Step 2.4.2

Multiply $4$ by $2$ .

$\frac{x (8 - 5)}{2} = 3 + \frac{3}{2} x + 4$

Step 2.4.3

Subtract $5$ from $8$ .

$\frac{x \cdot 3}{2} = 3 + \frac{3}{2} x + 4$

Step 2.5

Move $3$ to the left of $x$ .

$\frac{3 x}{2} = 3 + \frac{3}{2} x + 4$

Step 3

Simplify $3 + \frac{3}{2} x + 4$ .

Tap for more steps...

Step 3.1

Combine $\frac{3}{2}$ and $x$ .

$\frac{3 x}{2} = 3 + \frac{3 x}{2} + 4$

Step 3.2

Add $3$ and $4$ .

$\frac{3 x}{2} = \frac{3 x}{2} + 7$

Step 4

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 4.1

Subtract $\frac{3 x}{2}$ from both sides of the equation.

$\frac{3 x}{2} - \frac{3 x}{2} = 7$

Step 4.2

Subtract $\frac{3 x}{2}$ from $\frac{3 x}{2}$ .

$0 = 7$

Step 5

Since $0 \neq 7$ , there are no solutions.

No solution