Pre-Algebra Examples

$y = \frac{x}{4} - \frac{7}{4}$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Find the LCD of $\frac{x}{4}$ and $\frac{7}{4}$ .

Tap for more steps...

Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$4, 4$

Step 2.2

Since $4, 4$ contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part $4, 4$ then find LCM for the variable part .

Step 2.3

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

Step 2.4

$4$ has factors of $2$ and $2$ .

$2 \cdot 2$

Step 2.5

Multiply $2$ by $2$ .

$4$

Step 3

Multiply both sides by $4$ .

$4 y = 4 (\frac{x}{4} - \frac{7}{4})$

Step 4

Simplify the right side.

Tap for more steps...

Step 4.1

Simplify $4 (\frac{x}{4} - \frac{7}{4})$ .

Tap for more steps...

Step 4.1.1

Apply the distributive property.

$4 y = 4 \frac{x}{4} + 4 (- \frac{7}{4})$

Step 4.1.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.1.2.1

Cancel the common factor.

$4 y = 4 \frac{x}{4} + 4 (- \frac{7}{4})$

Step 4.1.2.2

Rewrite the expression.

$4 y = x + 4 (- \frac{7}{4})$

Step 4.1.3

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.1.3.1

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$4 y = x + 4 (\frac{- 7}{4})$

Step 4.1.3.2

Cancel the common factor.

$4 y = x + 4 (\frac{- 7}{4})$

Step 4.1.3.3

Rewrite the expression.

$4 y = x - 7$

Step 5

Rewrite the equation.

$x - 7 = 4 y$

Step 6

Move all terms containing variables to the left side of the equation.

Tap for more steps...

Step 6.1

Subtract $4 y$ from both sides of the equation.

$x - 7 - 4 y = 0$

Step 6.2

Move $- 7$ .

$x - 4 y - 7 = 0$

Step 7

Add $7$ to both sides of the equation.

$x - 4 y = 7$

Step 8