Algebra Examples

$7 \frac{1}{4} x + x - 2 \frac{11}{12} x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $7 \frac{1}{4} x + x - 2 \frac{11}{12} x + 1 \frac{2}{3} x$ .

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Step 1.1.1

Convert $7 \frac{1}{4}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$(7 + \frac{1}{4}) x + x - 2 \frac{11}{12} x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1.1.1.2

Add $7$ and $\frac{1}{4}$ .

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Step 1.1.1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(7 \cdot \frac{4}{4} + \frac{1}{4}) x + x - 2 \frac{11}{12} x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1.1.1.2.2

Combine $7$ and $\frac{4}{4}$ .

$(\frac{7 \cdot 4}{4} + \frac{1}{4}) x + x - 2 \frac{11}{12} x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{7 \cdot 4 + 1}{4} x + x - 2 \frac{11}{12} x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $7$ by $4$ .

$\frac{28 + 1}{4} x + x - 2 \frac{11}{12} x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1.1.1.2.4.2

Add $28$ and $1$ .

$\frac{29}{4} x + x - 2 \frac{11}{12} x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1.1.2

Convert $2 \frac{11}{12}$ to an improper fraction.

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Step 1.1.2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{29}{4} x + x - (2 + \frac{11}{12}) x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1.1.2.2

Add $2$ and $\frac{11}{12}$ .

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Step 1.1.2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{29}{4} x + x - (2 \cdot \frac{12}{12} + \frac{11}{12}) x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1.1.2.2.2

Combine $2$ and $\frac{12}{12}$ .

$\frac{29}{4} x + x - (\frac{2 \cdot 12}{12} + \frac{11}{12}) x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{29}{4} x + x - \frac{2 \cdot 12 + 11}{12} x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $2$ by $12$ .

$\frac{29}{4} x + x - \frac{24 + 11}{12} x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1.1.2.2.4.2

Add $24$ and $11$ .

$\frac{29}{4} x + x - \frac{35}{12} x + 1 \frac{2}{3} x = 5 \frac{3}{5}$

Step 1.1.3

Convert $1 \frac{2}{3}$ to an improper fraction.

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Step 1.1.3.1

A mixed number is an addition of its whole and fractional parts.

$\frac{29}{4} x + x - \frac{35}{12} x + (1 + \frac{2}{3}) x = 5 \frac{3}{5}$

Step 1.1.3.2

Add $1$ and $\frac{2}{3}$ .

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Step 1.1.3.2.1

Write $1$ as a fraction with a common denominator.

$\frac{29}{4} x + x - \frac{35}{12} x + (\frac{3}{3} + \frac{2}{3}) x = 5 \frac{3}{5}$

Step 1.1.3.2.2

Combine the numerators over the common denominator.

$\frac{29}{4} x + x - \frac{35}{12} x + \frac{3 + 2}{3} x = 5 \frac{3}{5}$

Step 1.1.3.2.3

Add $3$ and $2$ .

$\frac{29}{4} x + x - \frac{35}{12} x + \frac{5}{3} x = 5 \frac{3}{5}$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

Combine $\frac{29}{4}$ and $x$ .

$\frac{29 x}{4} + x - \frac{35}{12} x + \frac{5}{3} x = 5 \frac{3}{5}$

Step 1.1.4.2

Combine $x$ and $\frac{35}{12}$ .

$\frac{29 x}{4} + x - \frac{x \cdot 35}{12} + \frac{5}{3} x = 5 \frac{3}{5}$

Step 1.1.4.3

Move $35$ to the left of $x$ .

$\frac{29 x}{4} + x - \frac{35 \cdot x}{12} + \frac{5}{3} x = 5 \frac{3}{5}$

Step 1.1.4.4

Combine $\frac{5}{3}$ and $x$ .

$\frac{29 x}{4} + x - \frac{35 x}{12} + \frac{5 x}{3} = 5 \frac{3}{5}$

Step 1.1.5

Find the common denominator.

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Step 1.1.5.1

Multiply $\frac{29 x}{4}$ by $\frac{3}{3}$ .

$\frac{29 x}{4} \cdot \frac{3}{3} + x - \frac{35 x}{12} + \frac{5 x}{3} = 5 \frac{3}{5}$

Step 1.1.5.2

Multiply $\frac{29 x}{4}$ by $\frac{3}{3}$ .

$\frac{29 x \cdot 3}{4 \cdot 3} + x - \frac{35 x}{12} + \frac{5 x}{3} = 5 \frac{3}{5}$

Step 1.1.5.3

Write $x$ as a fraction with denominator $1$ .

$\frac{29 x \cdot 3}{4 \cdot 3} + \frac{x}{1} - \frac{35 x}{12} + \frac{5 x}{3} = 5 \frac{3}{5}$

Step 1.1.5.4

Multiply $\frac{x}{1}$ by $\frac{12}{12}$ .

$\frac{29 x \cdot 3}{4 \cdot 3} + \frac{x}{1} \cdot \frac{12}{12} - \frac{35 x}{12} + \frac{5 x}{3} = 5 \frac{3}{5}$

Step 1.1.5.5

Multiply $\frac{x}{1}$ by $\frac{12}{12}$ .

$\frac{29 x \cdot 3}{4 \cdot 3} + \frac{x \cdot 12}{12} - \frac{35 x}{12} + \frac{5 x}{3} = 5 \frac{3}{5}$

Step 1.1.5.6

Multiply $\frac{5 x}{3}$ by $\frac{4}{4}$ .

$\frac{29 x \cdot 3}{4 \cdot 3} + \frac{x \cdot 12}{12} - \frac{35 x}{12} + \frac{5 x}{3} \cdot \frac{4}{4} = 5 \frac{3}{5}$

Step 1.1.5.7

Multiply $\frac{5 x}{3}$ by $\frac{4}{4}$ .

$\frac{29 x \cdot 3}{4 \cdot 3} + \frac{x \cdot 12}{12} - \frac{35 x}{12} + \frac{5 x \cdot 4}{3 \cdot 4} = 5 \frac{3}{5}$

Step 1.1.5.8

Reorder the factors of $4 \cdot 3$ .

$\frac{29 x \cdot 3}{3 \cdot 4} + \frac{x \cdot 12}{12} - \frac{35 x}{12} + \frac{5 x \cdot 4}{3 \cdot 4} = 5 \frac{3}{5}$

Step 1.1.5.9

Multiply $3$ by $4$ .

$\frac{29 x \cdot 3}{12} + \frac{x \cdot 12}{12} - \frac{35 x}{12} + \frac{5 x \cdot 4}{3 \cdot 4} = 5 \frac{3}{5}$

Step 1.1.5.10

Multiply $3$ by $4$ .

$\frac{29 x \cdot 3}{12} + \frac{x \cdot 12}{12} - \frac{35 x}{12} + \frac{5 x \cdot 4}{12} = 5 \frac{3}{5}$

Step 1.1.6

Combine the numerators over the common denominator.

$\frac{29 x \cdot 3 + x \cdot 12 - 35 x + 5 x \cdot 4}{12} = 5 \frac{3}{5}$

Step 1.1.7

Simplify each term.

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Step 1.1.7.1

Multiply $3$ by $29$ .

$\frac{87 x + x \cdot 12 - 35 x + 5 x \cdot 4}{12} = 5 \frac{3}{5}$

Step 1.1.7.2

Move $12$ to the left of $x$ .

$\frac{87 x + 12 \cdot x - 35 x + 5 x \cdot 4}{12} = 5 \frac{3}{5}$

Step 1.1.7.3

Multiply $4$ by $5$ .

$\frac{87 x + 12 x - 35 x + 20 x}{12} = 5 \frac{3}{5}$

Step 1.1.8

Simplify terms.

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Step 1.1.8.1

Add $87 x$ and $12 x$ .

$\frac{99 x - 35 x + 20 x}{12} = 5 \frac{3}{5}$

Step 1.1.8.2

Subtract $35 x$ from $99 x$ .

$\frac{64 x + 20 x}{12} = 5 \frac{3}{5}$

Step 1.1.8.3

Add $64 x$ and $20 x$ .

$\frac{84 x}{12} = 5 \frac{3}{5}$

Step 1.1.8.4

Cancel the common factor of $84$ and $12$ .

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Step 1.1.8.4.1

Factor $12$ out of $84 x$ .

$\frac{12 (7 x)}{12} = 5 \frac{3}{5}$

Step 1.1.8.4.2

Cancel the common factors.

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Step 1.1.8.4.2.1

Factor $12$ out of $12$ .

$\frac{12 (7 x)}{12 (1)} = 5 \frac{3}{5}$

Step 1.1.8.4.2.2

Cancel the common factor.

$\frac{12 (7 x)}{12 \cdot 1} = 5 \frac{3}{5}$

Step 1.1.8.4.2.3

Rewrite the expression.

$\frac{7 x}{1} = 5 \frac{3}{5}$

Step 1.1.8.4.2.4

Divide $7 x$ by $1$ .

$7 x = 5 \frac{3}{5}$

Step 2

Simplify the right side.

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Step 2.1

Convert $5 \frac{3}{5}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$7 x = 5 + \frac{3}{5}$

Step 2.1.2

Add $5$ and $\frac{3}{5}$ .

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Step 2.1.2.1

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

$7 x = 5 \cdot \frac{5}{5} + \frac{3}{5}$

Step 2.1.2.2

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

$7 x = \frac{5 \cdot 5}{5} + \frac{3}{5}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$7 x = \frac{5 \cdot 5 + 3}{5}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $5$ by $5$ .

$7 x = \frac{25 + 3}{5}$

Step 2.1.2.4.2

Add $25$ and $3$ .

$7 x = \frac{28}{5}$

Step 3

Divide each term in $7 x = \frac{28}{5}$ by $7$ and simplify.

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Step 3.1

Divide each term in $7 x = \frac{28}{5}$ by $7$ .

$\frac{7 x}{7} = \frac{\frac{28}{5}}{7}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $7$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{\frac{28}{5}}{7}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{28}{5}}{7}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{28}{5} \cdot \frac{1}{7}$

Step 3.3.2

Cancel the common factor of $7$ .

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Step 3.3.2.1

Factor $7$ out of $28$ .

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

Step 3.3.2.2

Cancel the common factor.

$x = \frac{7 \cdot 4}{5} \cdot \frac{1}{7}$

Step 3.3.2.3

Rewrite the expression.

$x = \frac{4}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{5}$

Decimal Form:

$x = 0.8$