Algebra Examples

$\frac{3}{4} c - \frac{1}{4} c + 3 = 7$

Step 1

Simplify $\frac{3}{4} c - \frac{1}{4} c + 3$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{3}{4}$ and $c$ .

$\frac{3 c}{4} - \frac{1}{4} c + 3 = 7$

Step 1.1.2

Combine $c$ and $\frac{1}{4}$ .

$\frac{3 c}{4} - \frac{c}{4} + 3 = 7$

$\frac{3 c}{4} - \frac{c}{4} + 3 = 7$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$3 + \frac{3 c - c}{4} = 7$

Step 1.2.2

Subtract $c$ from $3 c$ .

$3 + \frac{2 c}{4} = 7$

Step 1.2.3

Cancel the common factor of $2$ and $4$ .

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Step 1.2.3.1

Factor $2$ out of $2 c$ .

$3 + \frac{2 (c)}{4} = 7$

Step 1.2.3.2

Cancel the common factors.

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Step 1.2.3.2.1

Factor $2$ out of $4$ .

$3 + \frac{2 c}{2 \cdot 2} = 7$

Step 1.2.3.2.2

Cancel the common factor.

$3 + \frac{2 c}{2 \cdot 2} = 7$

Step 1.2.3.2.3

Rewrite the expression.

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

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

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

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

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

Step 2

Move all terms not containing $c$ to the right side of the equation.

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Step 2.1

Subtract $3$ from both sides of the equation.

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

Step 2.2

Subtract $3$ from $7$ .

$\frac{c}{2} = 4$

$\frac{c}{2} = 4$

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{c}{2} = 2 \cdot 4$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1

Cancel the common factor.

$2 \frac{c}{2} = 2 \cdot 4$

Step 4.1.1.2

Rewrite the expression.

$c = 2 \cdot 4$

$c = 2 \cdot 4$

$c = 2 \cdot 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $2$ by $4$ .

$c = 8$

$c = 8$

$c = 8$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$