Algebra Examples

$37 x + \frac{1}{2} - (x + \frac{1}{4}) = 9 (4 x - 7) + 5$

Step 1

Simplify $37 x + \frac{1}{2} - (x + \frac{1}{4})$ .

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Step 1.1

Apply the distributive property.

$37 x + \frac{1}{2} - x - \frac{1}{4} = 9 (4 x - 7) + 5$

Step 1.2

Subtract $x$ from $37 x$ .

$36 x + \frac{1}{2} - \frac{1}{4} = 9 (4 x - 7) + 5$

Step 1.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$36 x + \frac{1}{2} \cdot \frac{2}{2} - \frac{1}{4} = 9 (4 x - 7) + 5$

Step 1.4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$36 x + \frac{2}{2 \cdot 2} - \frac{1}{4} = 9 (4 x - 7) + 5$

Step 1.4.2

Multiply $2$ by $2$ .

$36 x + \frac{2}{4} - \frac{1}{4} = 9 (4 x - 7) + 5$

Step 1.5

Combine the numerators over the common denominator.

$36 x + \frac{2 - 1}{4} = 9 (4 x - 7) + 5$

Step 1.6

Subtract $1$ from $2$ .

$36 x + \frac{1}{4} = 9 (4 x - 7) + 5$

Step 2

Simplify $9 (4 x - 7) + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$36 x + \frac{1}{4} = 9 (4 x) + 9 \cdot - 7 + 5$

Step 2.1.2

Multiply $4$ by $9$ .

$36 x + \frac{1}{4} = 36 x + 9 \cdot - 7 + 5$

Step 2.1.3

Multiply $9$ by $- 7$ .

$36 x + \frac{1}{4} = 36 x - 63 + 5$

Step 2.2

Add $- 63$ and $5$ .

$36 x + \frac{1}{4} = 36 x - 58$

Step 3

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

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Step 3.1

Subtract $36 x$ from both sides of the equation.

$36 x + \frac{1}{4} - 36 x = - 58$

Step 3.2

Combine the opposite terms in $36 x + \frac{1}{4} - 36 x$ .

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Step 3.2.1

Subtract $36 x$ from $36 x$ .

$0 + \frac{1}{4} = - 58$

Step 3.2.2

Add $0$ and $\frac{1}{4}$ .

$\frac{1}{4} = - 58$

Step 4

Since $\frac{1}{4} \neq - 58$ , there are no solutions.

No solution